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We construct a map from the prestack of Tate objects over a commutative ring $k$ to the stack of $\mathbb{G}_{\rm m}$-gerbes. The result is obtained by combining the determinant map from the stack of perfect complexes as proposed by Sch\"urg-To\"en-Vezzosi with a relative $S_{\bullet}$-construction for Tate objects as studied by Braunling-Groechenig-Wolfson. Along the way we prove a result about the K-theory of vector bundles over a connective $\mathbb{E}_{\infty}$-ring spectrum which is possibly of independent interest., Comment: Section 2 rewritten, some results now hold more generally

We derive a simple functional equation with two catalytic variables characterising the generating function of 3-stack-sortable permutations. Using this functional equation, we extend the 174-term series to 1000 terms. From this series, we conjecture that the generating function behaves as $$W(t) \sim C_0(1-\mu_3 t)^\alpha \cdot \log^\beta(1-\mu_3 t), $$ so that $$[t^n]W(t)=w_n \sim \frac{c_0\mu_3^n}{ n^{(\alpha+1)}\cdot \log^\lambda{n}} ,$$ where $\mu_3 = 9.69963634535(30),$ $\alpha = 2.0 \pm 0.25.$ If $\alpha = 2$ exactly, then $\lambda = -\beta+1$, and we estimate $\beta \approx -2,$ but with a wide uncertainty of $\pm 1.$ If $\alpha$ is not an integer, then $\lambda=-\beta$, but we cannot give a useful estimate of $\beta$. The growth constant estimate (just) contradicts a conjecture of the first author that $$9.702 < \mu_3 \le 9.704.$$ We also prove a new rigorous lower bound of $\mu_3\geq 9.4854$, allowing us to disprove a conjecture of Bóna. We then further extend the series using differential-approximants to obtain approximate coefficients $O(t^{2000}),$ expected to be accurate to $20$ significant digits, and use the approximate coefficients to provide additional evidence supporting the results obtained from the exact coefficients.

We give a definition of full level structure on group schemes of the form $G\times G$, where $G$ is a finite flat commutative group scheme of rank $p$ over a $\mathbb{Z}_p$-scheme $S$ or, more generally, a truncated $p$-divisible group of height $1$. We show that there is no natural notion of full level structure over the stack of all finite flat commutative group schemes., 11 pages

Just as rank-metric or Gabidulin codes may be used to construct rate-diversity tradeoff optimal space-time codes, a recently introduced generalization for the sum-rank metric, linearized Reed-Solomon codes, accomplishes the same in the case of multiple fading blocks. We provide the first explicit construction of minimal-delay rate-diversity optimal multiblock space-time codes as an application of linearized Reed-Solomon codes. We then demonstrate in simulation an example of a 2-block 2-by-2 code which, with a small performance penalty—less than 1 dB at a codeword error rate of 1e-4—matches the bit rate of a full diversity alternative while using a much smaller transmitted constellation. A stack decoder for this code is then suggested.

The development of six online quizzes to support students’ study of an introductory mathematics masters module at The Open University is described and their use evaluated. The quizzes were implemented using the STACK online e-assessment system, which is powered by a computer-algebra engine. Evaluation of student feedback and an initial quantitative study of the effect of engaging with the quizzes on the final examinations marks suggest that further development of e-assessment at mathematics masters level is warranted.

A first comprehensive treatment on complex eigenmodes is presented for general lossy traveling-wave electromagnetic structures where the per unit length propagation phase shift ($\beta$) dependent complex eigenfrequencies $\Omega(\beta)$ are mapped to the frequency dependent complex propagation constant $\gamma(\omega_0)$ for variety of electromagnetic structures. Rigorous procedures are presented to first compute the complex eigenmodes of both uniform and periodic electromagnetic structures which are confirmed using full-wave simulations and known analytical results. Two mapping procedures are further presented for arbitrary uniform and periodic structures, where the known $\{\Omega-\beta\}$ relationship is expressed using polynomial and Fourier series expansions, respectively. Consequently replacing $\{\Omega,~j\beta\}$ with $\{\omega_0, \gamma\}$ in the known $\{\Omega-\beta\}$ relation, a characteristic equation is formed which is then numerically solved for the two unknowns, representing the physical dispersion relation $\omega_0(\beta)$ and the frequency dependent propagation loss $\alpha(\omega_0)$ of the structure. The mapping procedure is demonstrated for variety of cases including unbounded uniform media, rectangular waveguide, Drude dispersive metamaterial and a periodic dielectric stack, where exact propagation characteristics have been successfully retrieved in all cases across both passbands and stopbands across frequency., Comment: 13 pages, 8 figures

In this paper we give a complete description of the integral Chow ring of the stack $\mathscr{H}_{g,1}$ of 1-pointed hyperelliptic curves, lifting relations and generators from the Chow ring of $\mathscr{H}_g$. We also give a geometric interpretation for the generators.

We previously showed that the fundamental groupoid of a topological space can be defined by the Seifert–van Kampen theorem. This allowed us to give the first axiomatization of the topological fundamental groupoid. We will prove in this paper that the analogue holds for the étale fundamental groupoid of a Noetherian scheme $X$ as well.

Suppose $(X,\Omega,g)$ is a compact Spin(7)-manifold, e.g. a Riemannian 8-manifold with holonomy Spin(7), or a Calabi-Yau 4-fold. Let $G$ be U$(m)$ or SU$(m)$, and $P\to X$ be a principal $G$-bundle. We show that the infinite-dimensional moduli space ${\mathcal B}_P$ of all connections on $P$ modulo gauge is orientable, in a certain sense. We deduce that the moduli space ${\mathcal M}_P^{Spin(7)}\subset{\mathcal B}_P$ of irreducible Spin(7)-instanton connections on $P$ modulo gauge, as a manifold or derived manifold, is orientable. This improves theorems of Cao and Leung arXiv:1502.01141 and Mu\~noz and Shahbazi arXiv:1707.02998. If $X$ is a Calabi-Yau 4-fold, the derived moduli stack $\boldsymbol{\mathscr M}$ of (complexes of) coherent sheaves on $X$ is a $-2$-shifted symplectic derived stack $(\boldsymbol{\mathcal M},\omega)$ by Pantev-To\"en-Vaqui\'e-Vezzosi arXiv:1111.3209, and so has a notion of orientation by Borisov-Joyce arXiv:1504.00690. We prove that $(\boldsymbol{\mathscr M},\omega)$ is orientable, by relating algebro-geometric orientations on $(\boldsymbol{\mathscr M},\omega)$ to differential-geometric orientations on ${\mathcal B}_P$ for U$(m)$-bundles $P\to X$, and using orientability of ${\mathcal B}_P$. This has applications to the programme of defining Donaldson-Thomas type invariants counting moduli spaces of (semi)stable coherent sheaves on a Calabi-Yau 4-fold, as in Donaldson and Thomas 1998, Cao and Leung arXiv:1407.7659, and Borisov and Joyce arXiv:1504.00690. This is the third in a series arXiv:1811.01096, arXiv:1811.02405 on orientations of gauge-theoretic moduli spaces., Comment: 57 pages. (v2) Major rewrite: new title, added author, new material on Calabi-Yau manifolds

Let $\mathcal D_n$ denote the average number of iterations of West's stack-sorting map $s$ that are needed to sort a permutation in $S_n$ into the identity permutation $123\cdots n$. We prove that \[0.62433\approx\lambda\leq\liminf_{n\to\infty}\frac{\mathcal D_n}{n}\leq\limsup_{n\to\infty}\frac{\mathcal D_n}{n}\leq \frac{3}{5}(7-8\log 2)\approx 0.87289,\] where $\lambda$ is the Golomb-Dickman constant. Our lower bound improves upon West's lower bound of $0.23$, and our upper bound is the first improvement upon the trivial upper bound of $1$. We then show that fertilities of permutations increase monotonically upon iterations of $s$. More precisely, we prove that $|s^{-1}(\sigma)|\leq|s^{-1}(s(\sigma))|$ for all $\sigma\in S_n$, where equality holds if and only if $\sigma=123\cdots n$. This is the first theorem that manifests a law-of-diminishing-returns philosophy for the stack-sorting map that B\'ona has proposed. Along the way, we note some connections between the stack-sorting map and the right and left weak orders on $S_n$., Comment: 17 pages, 4 figures

Flip-sort is a natural sorting procedure which raises fascinating combinatorial questions. It finds its roots in the seminal work of Knuth on stack-based sorting algorithms and leads to many links with permutation patterns. We present several structural, enumerative, and algorithmic results on permutations that need few (resp. many) iterations of this procedure to be sorted. In particular, we give the shape of the permutations after one iteration, and characterize several families of permutations related to the best and worst cases of flip-sort. En passant, we also give some links between pop-stack sorting, automata, and lattice paths, and introduce several tactics of bijective proofs which have their own interest., Comment: This v3 just updates the journal reference, according to the publisher wish

We compute the integral Chow ring of the stack of smooth, non-hyperelliptic curves of genus three. We obtain this result by computing the integral Chow ring of the stack of smooth plane quartics, by means of equivariant intersection theory., Comment: 40 pages, comments are welcome! To appear on Transactions of the American Mathematical Society

Stateful hash-based signature schemes are among the most efficient approaches for post-quantum signature schemes. Although not suitable for general use, they may be suitable for some use cases on constrained devices. LMS and XMSS are hash-based signature schemes that are conjectured to be quantum secure. In this work, we compared multiple instantiations of both schemes on an ARM Cortex-M4. More precisely, we compared performance, stack consumption, and other figures for key generation, signing and verifying. To achieve this, we evaluated LMS and XMSS using optimised implementations of SHA-256, SHAKE256, Gimli-Hash, and different variants of Keccak. Furthermore, we present slightly optimised implementations of XMSS achieving speedups of up to \(3.11{\times }\) for key generation, \(3.11{\times }\) for signing, and \(4.32{\times }\) for verifying.

This paper presents the most recent additions to the vitrivr multimedia retrieval stack made in preparation for the participation to the 9\(^{th}\) Video Browser Showdown (VBS) in 2020. In addition to refining existing functionality and adding support for classical Boolean queries and metadata filters, we also completely replaced our storage engine \(\textsf {ADAM}_{pro}\) by a new database called Cottontail DB. Furthermore, we have added support for scoring based on the temporal ordering of multiple video segments with respect to a query formulated by the user. Finally, we have also added a new object detection module based on Faster-RCNN and use the generated features for object instance search.

We consider the stack $\mathcal{L}og_X$ parametrizing log schemes over a log scheme $X$, and weak and strong properties of log morphisms via $\mathcal{L}og_X$, as defined by Olsson. We give a concrete combinatorial presentation of $\mathcal{L}og_X$, and prove a simple criterion of when weak and strong properties of log morphisms coincide. We then apply this result to the study of logarithmic regularity, derive its main properties, and give a chart criterion analogous to Kato's chart criterion of logarithmic smoothness., Comment: 19 pages, final version

We describe a family of graphs with queue-number at most 4 but unbounded stack-number. This resolves open problems of Heath, Leighton and Rosenberg (1992) and Blankenship and Oporowski (1999).

We construct Bridgeland stability conditions on the derived category of smooth quasi-projective Deligne-Mumford surfaces whose coarse moduli spaces have ADE singularities. This unifies the construction for smooth surfaces and Bridgeland's work on Kleinian singularities. The construction hinges on an orbifold version of the Bogomolov-Gieseker inequality for slope semistable sheaves on the stack, and makes use of the To\"en-Hirzebruch-Riemann-Roch theorem., Comment: 22 pages, comments are welcome! Final version, to appear in Math. Z. Section 5 rewritten, Appendix removed and submitted independently as arXiv:2103.10767

Layered pathwidth is a new graph parameter studied by Bannister et al (2015). In this paper we present two new results relating layered pathwidth to two types of linear layouts. Our first result shows that, for any graph $G$, the stack number of $G$ is at most four times the layered pathwidth of $G$. Our second result shows that any graph $G$ with track number at most three has layered pathwidth at most four. The first result complements a result of Dujmovi\'c and Frati (2018) relating layered treewidth and stack number. The second result solves an open problem posed by Bannister et al (2015)., Comment: 14 pages; 8 figures

In this paper, which is a sequel of arXiv:2002.07494, we investigate, for any reductive group $G$ over an algebraically closed field $k$, the Picard group of the universal moduli stack $\mathrm{Bun}_{G,g,n}$ of $G$-bundles over $n$-pointed smooth projective curves of genus $g$. In particular: we give new functorial presentations of the Picard group of $\mathrm{Bun}_{G,g,n}$; we study the restriction homomorphism onto the Picard group of the moduli stack of principal $G$-bundles over a fixed smooth curve; we determine the Picard group of the rigidification of $\mathrm{Bun}_{G,g,n}$ by the center of $G$ as well as the image of the obstruction homomorphism of the associated gerbe. As a consequence, we compute the divisor class group of the moduli space of semistable $G$-bundles over $n$-pointed smooth projective curves of genus $g$., Comment: 56 pages. Final version, to appear on Ann. Sc. Norm. Super. Pisa

Visibly pushdown transducers ( VPT ) extend visibly pushdown automata (VPA) with outputs. They read nested words, i.e. finite words on a structured alphabet partitioned into call, return and internal symbols, and produce output words, which are not necessarily nested. As for VPA , the behavior of the stack is synchronized with the types of input symbols: on reading a call symbol, exactly one stack symbol is pushed onto the stack; on reading a return symbol, exactly one stack symbol is popped from the stack; and the stack is untouched when reading internal symbols. Along their transitions VPT can append words on their output tape, whose concatenation define the resulting output word. Therefore VPT define transformations from nested words to words and can be seen as a subclass of pushdown transducers. In this paper, we study the algorithmic, closure and expressiveness properties of VPT .

In this paper we study the moduli stack of complexes of vector bundles (with chain isomorphisms) over a smooth projective variety X via derived algebraic geometry. We prove that if X is a Calabi–Yau variety of dimension d then this moduli stack has a ( 1 − d ) -shifted Poisson structure. In the case d = 1 , we construct a natural foliation of the moduli stack by 0-shifted symplectic substacks. We show that our construction recovers various known Poisson structures associated to complex elliptic curves, including the Poisson structure on Hilbert scheme of points on elliptic quantum projective planes studied by Nevins and Stafford, and the Poisson structures on the moduli spaces of stable triples over an elliptic curves considered by one of us. We also relate the latter Poisson structures to the semi-classical limits of the elliptic Sklyanin algebras studied by Feigin and Odesskii.

A general conjecture is stated on the cone of automorphic vector bundles admitting nonzero global sections on schemes endowed with a smooth, surjective morphism to a stack of$G$-zips of connected Hodge type; such schemes should include all Hodge-type Shimura varieties with hyperspecial level. We prove our conjecture for groups of type$A_{1}^{n}$,$C_{2}$, and$\mathbf{F}_{p}$-split groups of type$A_{2}$(this includes all Hilbert–Blumenthal varieties and should also apply to Siegel modular$3$-folds and Picard modular surfaces). An example is given to show that our conjecture can fail for zip data not of connected Hodge type.

Let $\overline{\mathcal{M}}_{g,A[n]}$ be the Hassett moduli stack of weighted stable curves, and let $\overline{M}_{g,A[n]}$ be its coarse moduli space. These are compactifications of $\mathcal{M}_{g,n}$ and $M_{g,n}$ respectively, obtained by assigning rational weights $A = (a_{1},...,a_{n})$, $0< a_{i} \leq 1$ to the markings; they are defined over $\mathbb{Z}$, and therefore over any field. We study the first order infinitesimal deformations of $\overline{\mathcal{M}}_{g,A[n]}$ and $\overline{M}_{g,A[n]}$. In particular, we show that $\overline{M}_{0,A[n]}$ is rigid over any field, if $g\geq 1$ then $\overline{\mathcal{M}}_{g,A[n]}$ is rigid over any field of characteristic zero, and if $g+n > 4$ then the coarse moduli space $\overline{M}_{g,A[n]}$ is rigid over an algebraically closed field of characteristic zero. Finally, we take into account a degeneration of Hassett spaces parametrizing rational curves obtained by allowing the weights to have sum equal to two. In particular, we consider such a Hassett $3$-fold which is isomorphic to the Segre cubic hypersurface in $\mathbb{P}^4$, and we prove that its family of first order infinitesimal deformations is non-singular of dimension ten, and the general deformation is smooth., 14 pages

In this note, we give explicit examples of compact complex 3-folds which admit automorphisms that are isotopic to the identity through C $\infty$-diffeomorphisms but not through biholomorphisms. These automorphisms play an important role in the construction of the Te-ichm{\"u}ller stack of higher dimensional manifolds., Comment: v2. Section 2 added (motivation)

We study the stack M of cameral covers for a complex reductive group G, introduced by Donagi and Gaitsgory. We compute its rational cohomology ring. In the special case G=GL(n), M is the stack of spectral covers. We also compute the cohomology ring of the stack of abstract regular G-Higgs bundles., 30 pages

For each simply connected, simple complex group $G$ we show that the direct sum of all vector bundles of conformal blocks on the moduli stack $\bar{\mathcal{M}}_{g, n}$ of stable marked curves carries the structure of a flat sheaf of commutative algebras. The fiber of this sheaf over a smooth marked curve $(C, \vec{p})$ agrees with the Cox ring of the moduli of quasi-parabolic principal $G-$bundles on $(C, \vec{p})$. We use the factorization rules on conformal blocks to produce flat degenerations of these algebras. These degenerations are toric in the case $G = SL_2(\mathbb{C}),$ and the resulting toric varieties are shown to be isomorphic to phylogenetic algebraic varieties from mathematical biology. We conclude with a proof that the Cox ring of the moduli stack of qausi-parabolic $SL_2(\mathbb{C})$ principal bundles over a generic curve is generated by conformal blocks of levels 1 and 2 with relations generated in degrees $2, 3,$ and 4.

We study 4d $$ \mathcal{N} $$ N = 1 supersymmetric theories of class $$ {\mathcal{S}}_k $$ S k , obtained from flux compactifications on a Riemann surface of 6d (1, 0) conformal theories describing the low energy physics on a stack of M5 branes probing a $$ \frac{@}{@}{\mathrm{\mathbb{Z}}}_k $$ @ @ ℤ k singularity. We conjecture that the protected spectrum of class $$ {\mathcal{S}}_k $$ S k theories contains a freely generated ring, generalizing the Coulomb branch of the $$ \mathcal{N} $$ N = 2 theories. We derive this by examining a limit of the supersymmetric index of 4d $$ \mathcal{N} $$ N = 1 class $$ {\mathcal{S}}_k $$ S k theories. The limit generalizes the Coulomb limit of $$ \mathcal{N} $$ N = 2 theories, which coincides with the case of k = 1 for a particular choice of flux. We conjecture a general simple formula for the index in the aforementioned limit.

A classical result by Ramalingam about synchronization-sensitive interprocedural program analysis implies that reachability for concurrent threads running recursive procedures is undecidable. A technique proposed by Qadeer and Rehof, to bound the number of context switches allowed between the threads, leads to an incomplete solution that is, however, believed to catch “most bugs” in practice. The question whether the technique can also prove the absence of bugs at least in some cases has remained largely open. In this paper we introduce a broad verification methodology for resource-parameterized programs that observes how changes to the resource parameter affect the behavior of the program. Applied to the context-unbounded analysis problem (CUBA), the methodology results in partial verification techniques for procedural concurrent programs. Our solutions may not terminate, but are able to both refute and prove context-unbounded safety for concurrent recursive threads. We demonstrate the effectiveness of our method using a variety of examples, the safe of which cannot be proved safe by earlier, context-bounded methods.

Progress in linking between the disparate levels of cognitive description and neural implementation requires explicit, testable, computationally based hypotheses. One such hypothesis is the dendrophilia hypothesis, which suggests that human syntactic abilities rely on our supra-regular computational abilities, implemented via an auxiliary memory store (a ‘stack’) centred on Broca's region via its connections with other cortical areas. Because linguistic phonology requires less powerful computational abilities than this, at the finite-state level, I suggest that there may be continuity between animal rule learning and human phonology, and that the circuits underlying this provided the precursors of our unusual syntactic abilities.

A literary theorist, a biologist, an historian, a writing studies scholar, and a poet walk into a wine bar. The poet says, “I’ve got a stack of 1,223 handwritten questionnaire responses here in my bag; would you like to have a look?” The others reply, “Sure. Let’s see what we can learn here.” Descending from their respective disciplinary perches, they all gather around a table and start sifting through the questionnaires, which chronicle the writing background, habits, and emotions of PhD students and faculty in 15 countries. In this single corpus of data, each researcher sees something different, and from the other researchers’ responses, each learns new ways of seeing. What counts as an appropriate data analysis? What, for that matter, counts as data? We invite you to grab a drink and join our conversation.

We study the class of binary coded versions of unary languages that can be accepted by alternating machines with loglog n space. We show that there exists a binary PSpace-complete language $\mathcal {L}$ such that the unary coded version of $\mathcal {L}$ is in ASpace(loglog n). Consequently, the standard translation between unary languages accepted with loglog n space and binary languages accepted with log n space works for alternating machines if and only ifP = PSpace. In general, if a binary language is accepted deterministically in 2n⋅nO(1) time and, simultaneously, in nO(1) space—which covers many PSpace-complete problems—then its unary coded version is accepted by an alternating Turing machine using an initially delimited worktape of size loglog n. This unexpected power follows from the fact that, with an auxiliary worktape of size O(loglog n) on a unary input 1n, an alternating machine can simulate a stack with log n bits, representing the contents of the stack by its input head position. The standard push/pop operations on the stack are implemented by moving the head along the input.

Let X be a smooth projective curve over a field of characteristic zero. We calculate the motivic class of the moduli stack of semistable Higgs bundles on X. We also calculate the motivic class of the moduli stack of vector bundles with connections by showing that it is equal to the class of the stack of semistable Higgs bundles of the same rank and degree zero. We follow the strategy of Mozgovoy and Schiffmann for counting Higgs bundles over finite fields. The main new ingredient is a motivic version of a theorem of Harder about Eisenstein series claiming that all vector bundles have approximately the same motivic class of Borel reductions as the degree of Borel reduction tends to $-\infty$., Comment: Minor corrections and improvements; 48 pages

We consider the problem of reachability on One-Counter Systems (OCSs) and Pushdown Systems (PDSs). The problem has a well-known O ( n 3 ) bound on both models, while the bound is believed to be tight for PDSs. Here we establish new upper and lower bounds for reachability on OCSs and restricted PDSs. We show that the problem can be solved (i) in O ( n ω ⋅ log 2 ⁡ n ) time on OCSs, and (ii) in O ( n 2 ) time on sparse PDSs when restricted to witness executions of stack height bounded by log ⁡ n . Moreover, we prove similar lower bounds.

For a Calabi–Yau 4-fold ( X , ω ) , where X is quasi-projective and ω is a nowhere vanishing section of its canonical bundle K X , the (derived) moduli stack of compactly supported perfect complexes M X is −2-shifted symplectic and thus has an orientation bundle O ω → M X in the sense of Borisov–Joyce [11] necessary for defining Donaldson–Thomas type invariants of X. We extend first the orientability result of Cao–Gross–Joyce [23] to projective spin 4-folds. Then for any smooth projective compactification Y, such that D = Y ﹨ X is strictly normal crossing, we define orientation bundles on the stack M Y × M D M Y and express these as pullbacks of Z 2 -bundles in gauge theory, constructed using positive Dirac operators on the double of X. As a result, we relate the orientation bundle O ω → M X to a gauge-theoretic orientation on the classifying space of compactly supported K-theory. Using orientability of the latter, we obtain orientability of M X . We also prove orientability of moduli spaces of stable pairs and Hilbert schemes of proper subschemes. Finally, we consider the compatibility of orientations under direct sums.

Let G be a connected split reductive group over a field k of characteristic zero. Let $$X\rightarrow S$$ be a smooth projective morphism of k-schemes, with geometrically connected fibers. We formulate a natural definition of a relative canonical reduction, under which principal G-bundles of any given Harder–Narasimhan type $$\tau $$ on fibers of X / S form an Artin algebraic stack $$Bun_{X/S}^{\tau }(G)$$ over S, and as $$\tau $$ varies, these stacks define a stratification of the stack $$Bun_{X/S}(G)$$ by locally closed substacks. This result extends to principal bundles in higher dimensions the earlier such result for principal bundles on families of curves. The result is new even for vector bundles, that is, for $$G = GL_{n,k}$$ .

The purpose of this paper is to lay the foundations of a theory of invariants in \'etale cohomology for smooth Artin stacks. We compute the invariants in the case of the stack of elliptic curves, and we use the theory we developed to get some results regarding Brauer groups of algebraic spaces., Comment: final version

In Marr v Collie (Bahamas) [2017] UKPC 17, a Board of the Privy Council comprising Lord Neuberger, Lady Hale, and Lords Kerr, Wilson, and Sumption has interpreted Stack v Dowden [2007] UKHL 17; [2007] 2 A.C. 432 in a way that many may find surprising. However, on close examination Marr is a clear and correct interpretation of Stack, dispelling misunderstandings by returning to its ratio.

Stacks of ambient noise correlations are routinely used to extract empirical Green's functions (EGFs) between station pairs. The time-frequency phase-weighted stack (tf-PWS) is a physically intuitive nonlinear denoising method that uses the phase coherence to improve EGF convergence when the performance of conventional linear averaging methods is not sufficient. The high computational cost of a continuous approach to the time-frequency transformation is currently a main limitation in ambient noise studies. We introduce the time-scale phaseweighted stack (ts-PWS) as an alternative extension of the phase-weighted stack that uses complex frames of wavelets to build a time-frequency representation that is much more efficient and fast to compute and that preserve the performance and flexibility of the tf-PWS. In addition, we propose two strategies: the unbiased phase coherence and the two-stage ts-PWS methods to further improve noise attenuation, quality of the extracted signals and convergence speed. We demonstrate that these approaches enable to extract minor-and major-arc Rayleigh waves (up to the sixth Rayleigh wave train) from many years of data from the GEOSCOPE global network. Finally we also show that fundamental spheroidal modes can be extracted from these EGF., SV thanks the Secretaria d’Universitats i Recerca del Departament d’Economia i Coneixement de la Generalitat de Catalunya and the 7th European Framework Program Marie Curie COFUND - contract 600385; Beatriu de Pinós Fellowship. We acknowledge support from discussions within TIDES COST Actions ES1401. MS and SV also thank the Spanish MISTERIOS project CGL2013-48601-C2-1-R. ES was supported by the ANR MIMOSA project (ANR-16-CE33-0005).

We prove a general criterion for an algebraic stack to admit a good moduli space. This result may be considered as a generalization of the Keel–Mori theorem, which guarantees the existence of a coarse moduli space for a separated Deligne–Mumford stack. We apply this result to prove that the moduli stacks $\overline{{\mathcal{M}}}_{g,n}(\unicode[STIX]{x1D6FC})$ parameterizing $\unicode[STIX]{x1D6FC}$-stable curves introduced in [J. Alper et al., Second flip in the Hassett–Keel program: a local description, Compositio Math. 153 (2017), 1547–1583] admit good moduli spaces.

We construct simply connected surfaces of general type with invariants χ(O)=4 and 2≤K2≤8. We use Q-Gorenstein deformations in conjunction with explicit constructions that express the canonical rings by generators and relations. The canonical rings of the surfaces are described as projections. The whole construction is simplified by the use of key varieties based on Steiner 3-folds. As a consequence of the construction we find two families, each family in a different connected component of the moduli stack M¯2,1, and each linking a Campedelli surface with a Godeaux surface.

Let G be a simple simply-connected group over an algebraically closed field k, X be a smooth connected projective curve over k. In this paper we develop the theory of geometric Eisenstein series on the moduli stack Bun_G of G-torsors on X in the setting of the quantum geometric Langlands program (for \'etale l-adic sheaves) in analogy with [3]. We calculate the intersection cohomology sheaf on the version of Drinfeld compactification in our twisted setting. In the case G=SL_2 we derive some results about the Fourier coefficients of our Eisenstein series. In the case of G=SL_2 and X=P^1 we also construct the corresponding theta-sheaves and prove their Hecke property., Comment: 69 pages, v4: new results are added

We show that the failure of the usual Verdier duality on Bun(G) leads to a new duality functor on the category of D-modules, and we study its relation to the operation of Eisenstein series.

In this paper we study the homotopy limits of cosimplicial diagrams of dg-categories. We first give an explicit construction of the totalization of such a diagram and then show that the totalization agrees with the homotopy limit in the following two cases: (1) the complexes of sheaves of $\mathcal O$-modules on the \v{C}ech nerve of an open cover of a ringed space $(X, \mathcal O)$; (2) the complexes of sheaves on the simplicial nerve of a discrete group $G$ acting on a space. The explicit models we obtain in this way are twisted complexes as well as their $D$-module and $G$-equivariant versions. As an application we show that there is a stack of twisted perfect complexes., Comment: v3: 22 pages, minor changes, to appear in Homology, Homotopy and Applications. v2: a new subsection (Section 4.5) is added on the stack of twisted perfect complexes

The height filtration on the stack of formal groups $$\mathcal{M}$$ FG is well known. We explore analogous filtration on a set of morphisms of formal group laws, which extends to the stack $$\mathcal{M}$$ FG. It is correctly defined colimit object for this filtration which can be identified with the colimit $$\mathcal{M}$$ FG,∞. As a corollary we prove explicitly density of additive formal group in any group law.

We consider permutations sortable by $k$ passes through a deterministic pop stack. We show that for any $k\in\mathbb N$ the set is characterised by finitely many patterns, answering a question of Claesson and Gu{\dh}mundsson. Our characterisation demands a more precise definition than in previous literature of what it means for a permutation to avoid a set of barred and unbarred patterns. We propose a new notion called \emph{$2$-avoidance}., Comment: 10 pages, 4 figures. Simpler notion of 2-avoidance introduced, replacing the more complicated (but equivalent) PB-avoidance in the previous version

We investigate the moduli of genus 10 curves that are endowed with a faithful action of the icosahedral group $\mathcal{A}_5$. We show among other things that this has the structure of a Deligne-Mumford stack whose underlying coarse moduli space essentially consists of two copies of the pencil of plane sextics that was introduced by Winger in 1924, but with the unique unstable member (a triple conic) replaced by a smooth non-planar curve. The orbifold defined by any member has genus zero and comes with 4 orbifold points. We show that by numbering the points, we get a fine moduli space whose base is naturally a finite cover of $\Mcal_{0,4}$., To be appeared on European Journal of Mathematics

The $\mathcal{N}=1$ superconformal field theories that arise in AdS-CFT from placing a stack of D3-branes at the singularity of a toric Calabi-Yau threefold can be described succinctly by dimer models. We present an efficient algorithm for constructing a dimer model from the geometry of the Calabi-Yau. Since not all dimers produce consistent field theories, we perform several consistency checks on the field theories produced by our algorithm: they have the correct number of gauge groups, their cubic anomalies agree with the Chern-Simons coefficients in the AdS dual, and all gauge invariant chiral operators satisfy the unitarity bound. We also give bounds on the ratio of the central charge of the theory to the area of the toric diagram. To prove these results, we introduce the concept of a properly ordered dimer., 33 pages, 19 figures, some corrections and clarifications

We will calculate the essential dimension of the moduli stack of polarized K3 surfaces, including the positive char case., Some mistakes corrected

It follows from work of S. Mochizuki, F. Liu, and B. Osserman that there is a relationship between Ehrhart’s theory concerning rational polytopes and the geometry of the moduli stack classifying dormant indigenous bundles on a proper hyperbolic curve in positive characteristic. This relationship was established by considering the (finite) cardinality of the set consisting of certain colorings on a $3$ -regular graph called spin networks. In the present article, we recall the correspondences between spin networks, lattice points of rational polytopes, and dormant indigenous bundles and present some identities and explicit computations of invariants associated with the objects involved.