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Given Y a non-compact manifold or orbifold, we define a natural subspace of the cohomology of Y called the narrow cohomology. We show that despite Y being non-compact, there is a well-defined and non-degenerate pairing on this subspace. The narrow cohomology proves useful for the study of genus zero Gromov-Witten theory. When Y is a smooth complex variety or Deligne-Mumford stack, one can define a quantum D-module on the narrow cohomology of Y. This yields a new formulation of quantum Serre duality.

Consider the strong subordination of a multivariate Lévy process with a multivariate subordinator. If the subordinate is a stack of independent Lévy processes and the components of the subordinator are indistinguishable within each stack, then strong subordination produces a Lévy process; otherwise it may not. Weak subordination was introduced to extend strong subordination, always producing a Lévy process even when strong subordination does not. Here we prove that strong and weak subordination are equal in law under the aforementioned condition. In addition, we prove that if strong subordination is a Lévy process then it is necessarily equal in law to weak subordination in two cases: firstly when the subordinator is deterministic, and secondly when it is pure-jump with finite activity.

We construct a complex analytic version of an equivariant cohomology theory which appeared in a paper of Rezk, and which is roughly modelled on the Borel-equivariant cohomology of the double free loop space. The construction is defined on finite, torus-equivariant CW complexes and takes values in coherent holomorphic sheaves over the moduli stack of complex elliptic curves. Our methods involve an inverse limit construction over all finite-dimensional subcomplexes of the double free loop space, following an analogous construction of Kitchloo for single free loop spaces. We show that, for any given complex elliptic curve $\mathcal {C}$, the fiber of our construction over $\mathcal {C}$ is isomorphic to Grojnowski's equivariant elliptic cohomology theory associated to $\mathcal {C}$.

Let $\mathcal{KC}_g ^k$ be the moduli stack of pairs $(S,C)$ with $S$ a $K3$ surface and $C\subset S$ a genus $g$ curve with divisibility $k$ in $\mathrm{Pic}(S)$. In this article we study the forgetful map $c_g^k:(S,C) \mapsto C$ from $\mathcal{KC}_g ^k$ to $\mathcal{M}_g$ for $k>1$. First we compute by geometric means the dimension of its general fibre. This turns out to be interesting only when $S$ is a complete intersection or a section of a Mukai variety. In the former case we find the existence of interesting Fano varieties extending $C$ in its canonical embedding. In the latter case this is related to delicate modular properties of the Mukai varieties. Next we investigate whether $c_g^k$ dominates the locus in $\mathcal{M}_g$ of $k$-spin curves with the appropriate number of independent sections. We are able to do this only when $S$ is a complete intersection, and obtain in these cases some classification results for spin curves., v2: post-final version. Various enhancements in Sec.4 (including new subsection 4.4 on maximal variation) that will not appear in the published version, to appear in Boll. Unione Mat. Ital

We study the Hitchin map for Gℝ-Higgs bundles on a smooth curve, where Gℝ is a quasi-split real form of a complex reductive algebraic group G. By looking at the moduli stack of regular Gℝ-Higgs bundles, we prove that it induces a banded gerbe structure on a slightly larger stack, whose band is given by sheaves of tori. This characterization yields a cocyclic description of the fibres of the corresponding Hitchin map by means of cameral data. According to this, fibres of the Hitchin map are categories of principal torus bundles on the cameral cover. The corresponding points inside the stack of G-Higgs bundles are contained in the substack of points fixed by an involution induced by the Cartan involution of Gℝ. We determine this substack of fixed points and prove that stable points are in correspondence with stable Gℝ-Higgs bundles.

Let X be a compact connected Riemann surface of genus g, with $$g\, \ge \, 2$$ , and let $${\text {G}}$$ be a connected semisimple affine algebraic group defined over $${\mathbb {C}}$$ . Given any $$\delta \, \in \, \pi _1({\text {G}})$$ , we prove that the moduli space of semistable principal $${\text {G}}$$ -bundles over X of topological type $$\delta $$ is simply connected. More generally, if $${\text {G}}$$ is a connected reductive complex affine algebraic group, then the fundamental group of the moduli space is isomorphic to $${\mathbb Z}^{2gd}$$ , where d is the complex dimension of the center of $${\text {G}}$$ . In contrast, the fundamental group of the moduli stack of principal $${\text {G}}$$ -bundles over X of topological type $$\delta $$ is shown to be isomorphic to $$H^1(X,\, \pi _1({\text {G}}))$$ , when $${\text {G}}$$ is semisimple. We also compute the fundamental group of the moduli stack of principal $${\text {G}}$$ -bundles when $${\text {G}}$$ is reductive.

The number of users who have the appropriate knowledge to answer asked questions in community question answering is lower than those who ask questions. Therefore, finding expert users who can answer the questions is very crucial and useful. In this article, we propose a framework to find experts for given questions and assign them the related questions. The proposed model benefits from users’ relations in a community along with the lexical and semantic similarities between new question and existing answers. Node embedding is applied to the community graph to find similar users. Our experiments on four different Stack Exchange datasets show that adding community relations improves the performance of expert finding models.

We give criteria for certain morphisms from an algebraic stack to a (not necessarily algebraic) stack to admit an (appropriately defined) scheme-theoretic image. We apply our criteria to show that certain natural moduli stacks of local Galois representations are algebraic (or Ind-algebraic) stacks., 137 pages; final version although not incorporating minor edits made in proof, appeared as Algebraic Geometry 8 (1) (2021) 1--132

Given a smooth projective variety $X$ and a smooth divisor $D\subset X$. We study relative Gromov-Witten invariants of $(X,D)$ and the corresponding orbifold Gromov-Witten invariants of the $r$-th root stack $X_{D,r}$. For sufficiently large $r$, we prove that orbifold Gromov-Witten invariants of $X_{D,r}$ are polynomials in $r$. Moreover, higher genus relative Gromov-Witten invariants of $(X,D)$ are exactly the constant terms of the corresponding higher genus orbifold Gromov-Witten invariants of $X_{D,r}$. We also provide a new proof for the equality between genus zero relative and orbifold Gromov-Witten invariants, originally proved by Abramovich-Cadman-Wise \cite{ACW}. When $r$ is sufficiently large and $X=C$ is a curve, we prove that stationary relative invariants of $C$ are equal to the stationary orbifold invariants in all genera., 29 pages. Revised according to referees' suggestions. Including results from arXiv:1804.09905 on target curves. To appear in Geometry & Topology

In this paper, we show that the numbers of t-stack sortable n-permutations with k − 1 descents satisfy central and local limit theorems for t = 1, 2, n − 1 and n − 2. This result, in particular, gives an affirmative answer to Shapiro's question about the asymptotic normality of the Narayana numbers.

We explicitly describe the KSBA/Hacking compactification of a moduli space of log surfaces of Picard rank 2. The space parametrizes log pairs $(S, D)$ where $S$ is a degeneration of $\mathbb{P}^1 \times \mathbb{P}^1$ and $D \subset S$ is a degeneration of a curve of class $(3,3)$. We prove that the compactified moduli space is a smooth Deligne--Mumford stack with 4 boundary components. We relate it to the moduli space of genus 4 curves; we show that it compactifies the blow-up of the hyperelliptic locus. We also relate it to a compactification of the Hurwitz space of triple coverings of $\mathbb{P}^1$ by genus 4 curves., 49 pages, 9 figures. Added more details and improved the introduction. To appear in Transactions of the American Mathematical Society

Watson-Crick automata work on two-stranded tape, and, consequently, they have two reading heads. In the case of sensing 5 ′ → 3 ′ Watson-Crick automata, the two heads start from different ends of the input and they move in opposite directions until they meet. In this paper, an extension of these automata is presented by adding a pushdown stack. This model can also be seen as a 2-head extension of the pushdown automata. Acceptance by empty stack and acceptance by final states are proven to have the same recognition power in this new model. The language family recognized by this model contains only semi-linear context-sensitive languages and it includes the class of context-free languages. Some well-known non-context-free languages are shown as examples. Normal form like results, a pumping lemma and various closure properties are also proven.

We define and study the motive of the moduli stack of vector bundles of fixed rank and degree over a smooth projective curve in Voevodsky's category of motives. We prove that this motive can be written as a homotopy colimit of motives of smooth projective Quot schemes of torsion quotients of sums of line bundles on the curve. When working with rational coefficients, we prove that the motive of the stack of bundles lies in the localising tensor subcategory generated by the motive of the curve, using Bialynicki-Birula decompositions of these Quot schemes. We conjecture a formula for the motive of this stack, and we prove this conjecture modulo a conjecture on the intersection theory of the Quot schemes., 32 pages. We have moved the section on Bialynicki-Birula decompositions (Section 3 in v1) to another joint paper entitled 'On the Voevodsky motive of the moduli space of Higgs bundles on a curve'

Given a strict simple degeneration $f \colon X\to C$ the first three authors previously constructed a degeneration $I^n_{X/C} \to C$ of the relative degree $n$ Hilbert scheme of $0$-dimensional subschemes. In this paper we investigate the geometry of this degeneration, in particular when the fibre dimension of $f$ is at most $2$. In this case we show that $I^n_{X/C} \to C$ is a dlt model. This is even a good minimal dlt model if $f \colon X \to C$ has this property. We compute the dual complex of the central fibre $(I^n_{X/C})_0$ and relate this to the essential skeleton of the generic fibre. For a type II degeneration of $K3$ surfaces we show that the stack ${\mathcal I}^n_{X/C} \to C$ carries a nowhere degenerate relative logarithmic $2$-form. Finally we discuss the relationship of our degeneration with the constructions of Nagai., Comment: 53 pages. To appear in J. Algebraic Geom

We study projective structures on a surface having poles of prescribed orders. We obtain a monodromy map from a complex manifold parameterising such structures to the stack of framed $\mathrm{PGL}_2(\mathbb{C})$ local systems on the associated marked bordered surface. We prove that the image of this map is contained in the union of the domains of the cluster charts. We discuss a number of open questions concerning this monodromy map., Comment: 54 pages. Version 2: Incorporated suggestions from referee

We give an algebraic analog of the functional equation of Riemann's theta function. More precisely, we define a `theta multiplier' line bundle over the moduli stack of principally polarized abelian schemes with theta characteristic and prove that its dual is isomorphic to the determinant bundle over the moduli stack. We do so by explicitly computing with Picard groups over the moduli stack. This is all done over the ring R=Z[1/2,i]: passing to the complex numbers, we recover the classical functional equation.

The purpose of the present paper is to develop the theory of (pre-)Tango structures and (dormant generic) Miura $\mathfrak{g}$-opers (for a semisimple Lie algebra $\mathfrak{g}$) defined on pointed stable curves in positive characteristic. A (pre-)Tango structure is a certain line bundle of an algebraic curve in positive characteristic, which gives some pathological (relative to zero characteristic) phenomena. In the present paper, we construct the moduli spaces of (pre-)Tango structures and (dormant generic) Miura $\mathfrak{g}$-opers respectively, and prove certain properties of them. One of the main results of the present paper states that there exists a bijective correspondence between the (pre-)Tango structures (of prescribed monodromy) and the dormant generic Miura $\mathfrak{s} \mathfrak{l}_2$-opers (of prescribed exponent). By means of this correspondence, we achieve a detailed understanding of the moduli stack of (pre-)Tango structures. As an application, we construct a family of algebraic surfaces in positive characteristic parametrized by a higher dimensional base space whose fibers are pairwise non-isomorphic and violate the Kodaira vanishing theorem., 74 pages, revised version

Let Y be a geometrically irreducible nodal projective algebraic curve of arithmetic genus $$g \ge 2$$ defined over $${{\mathbb {R}}}$$ . Let $$Y_{{\mathbb {C}}} = Y \times _{{\mathbb {R}}} {\mathbb {C}}$$ . Fix an $${\mathbb {R}}$$ -valued point $$\xi $$ of $$Pic^d(Y)$$ . For integers $$r \ge 2$$ and d, let $$M(r,\xi )$$ [respectively $$U(r,\xi )$$ ] be the moduli stack of vector bundles (respectively the moduli space of stable vector bundles) of rank r and determinant $$\xi $$ on Y. We determine the Picard group of $$M(r,\xi )$$ . We compute the Picard group and Brauer group of $$U(r,\xi )$$ .

Starting in the late 1930s Sullivan’s interpersonal theory became one of the main alternatives to Freud’s drive theory based on the vicissitudes of libidinal forces. In the United States, he was jo...

Nowadays Online question answering website platforms are getting popular as it allows the users to get responses from varied experts beyond their reach. Businesses use these sites for their growth and exposure. Enormous volumes of question are posted on these sites. Finding an expert for answering large voluminous questions requires specialized techniques. This paper proposes hybrid approach for finding prominent expert for the posted questions. The proposed approach uses clustering and social network metrics. The approach clusters the database questions based on tag similarity using K Means. The new posted question is matched with the clusters and best suitable cluster is extracted. Developer Social Network is constructed for chosen cluster and Page Rank with time decay has been applied to find the prominent developer. The proposed approach attains 60% accuracy.

For a gerbe $\mathcal{Y}$ over a smooth proper Deligne–Mumford stack $\mathcal{B}$ banded by a finite group $G$, we prove a structure result on the Gromov–Witten theory of $\mathcal{Y}$, expressing Gromov–Witten invariants of $\mathcal{Y}$ in terms of Gromov–Witten invariants of $\mathcal{B}$ twisted by various flat $U(1)$‑gerbes on $\mathcal{B}$. This can be viewed as a Leray–Hirsch type of result for Gromov–Witten theory of gerbes.

We establish an algebraic approach to prove the properness of moduli spaces of K-polystable Fano varieties and reduce the problem to a conjecture on destabilizations of K-unstable Fano varieties. Specifically, we prove that if the stability threshold of every K-unstable Fano variety is computed by a divisorial valuation, then such K-moduli spaces are proper. The argument relies on studying certain optimal destabilizing test configurations and constructing a $$\Theta $$ -stratification on the moduli stack of Fano varieties.

We study in this article the dual of a (strictly) commutative group stack $G$ and give some applications. Using the Picard functor and the Picard stack of $G$, we first give some sufficient conditions for $G$ to be dualizable. Then, for an algebraic stack $X$ with suitable assumptions, we define an Albanese morphism $a_X : X\to A^1(X)$ where $A^1(X)$ is a torsor under the dual commutative group stack $A^0(X)$ of $Pic_{X/S}$. We prove that $a_X$ satisfies a natural universal property. We give two applications of our Albanese morphism. On the one hand, we give a geometric description of the elementary obstruction and of universal torsors (standard tools in the study of rational varieties over number fields). On the other hand we give some examples of algebraic stacks that satisfy Grothendieck's section conjecture., 40 pages. Final version, including the comments of the referees. To appear in IMRN

First the Griffiths line bundle of a $\mathbf Q$-VHS $\mathscr V$ is generalized to a Griffiths character ${\rm grif}(\mathbf G, \mu,r)$ associated to any triple $(\mathbf G, \mu, r)$, where $\mathbf G$ is a connected reductive group over an arbitrary field $F$, $\mu \in X_*(\mathbf G)$ is a cocharacter (over $\overline{F}$) and $r:\mathbf G \to GL(V)$ is an $F$-representation; the classical bundle studied by Griffiths is recovered by taking $F=\mathbf Q$, $\mathbf G$ the Mumford-Tate group of $\mathscr V$, $r:\mathbf G \to GL(V)$ the tautological representation afforded by a very general fiber and pulling back along the period map the line bundle associated to ${\rm grif}(\mathbf G, \mu, r)$. The more general setting also gives rise to the Griffiths bundle in the analogous situation in characteristic $p$ given by a scheme mapping to a stack of $\mathbf G$-Zips. When $\mathbf G$ is $F$-simple, we show that, up to positive multiples, the Griffiths character ${\rm grif}(\mathbf G,\mu,r)$ (and thus also the Griffiths line bundle) is essentially independent of $r$ with central kernel, and up to some identifications is given explicitly by $-\mu$. As an application, we show that the Griffiths line bundle of a projective $\mathbf G{\rm -Zip}^{\mu}$-scheme is nef., Comment: Math. Ann., to appear

We find a new presentation of the stack of hyperelliptic curves of odd genus as a quotient stack and we use it to compute its integral Chow ring by means of equivariant intersection theory., Comment: 27 pages, published on Int. Math. Res. Not

We prove that the Brauer group of the moduli stack of elliptic curves M 1 , 1 , k over an algebraically closed field k of characteristic 2 is isomorphic to Z / ( 2 ) . We also compute the Brauer group of M 1 , 1 , k where k is a finite field of characteristic 2.

We present a defect spectroscopy technique to profile the energy and spatial distribution of defects within a material stack from leakage current ( ${J}$ – ${V}$ ), capacitance ( ${C}$ – ${V}$ ), and conductance ( ${G}$ – ${V}$ ) measurements. The technique relies on the concept of sensitivity maps (SMs) that identify the bandgap regions, where defects affect those electrical characteristics. The information provided by SMs are used to reproduce ${J}$ – ${V}$ , ${C}$ – ${V}$ , and ${G}$ – ${V}$ data measured at different temperatures and frequencies by means of physics-based simulations relying on an accurate description of carrier-defect interactions. The proposed defect spectroscopy technique is applied to ZrO2-based metal–insulator–metal structures of different compositions for dynamic random-access memory capacitor applications. The origin of the observed voltage, temperature, and frequency dependencies of the ${I}$ – ${V}$ , ${C}$ – ${V}$ , and ${G}$ – ${V}$ data is understood, and the atomic structure of the relevant stack defects is identified.

Inverter delay is often evaluated as $\textit {CV}_{\text {dd}}/{I}_{\text {eff}}$ , where ${C}$ is the load capacitance, ${V}_{\text {dd}}$ is the supply voltage, and ${I}_{\text {eff}}$ is the effective drive current derived by approximating the inverter switching trajectory with a linear model. The ${I}_{\text {eff}}$ model utilizes high and low drain currents conventionally measured in wafer acceptance tests and does not require extraction of any parameters. Ease of use combined with reasonable accuracy (~15%) is the main reason for wide application of $\textit {CV}_{\text {dd}}/{I}_{\text {eff}}$ delay metrics. However, $\textit {CV}_{\text {dd}}/{I}_{\text {eff}}$ expression produces large errors when applied to another two important basic circuits: NAND and NOR. This is because NAND and NOR circuits contain transistor series connections not accounted for in the inverter model. In this paper, an analytical solution for the transistor series connection influence on the discharge/charge operation in NAND/NOR circuits is provided. The model for NAND/NOR effective drive current (denoted as ${I}_{\text {stack}}$ ) developed in this paper maintains simplicity of the original ${I}_{\text {eff}}$ expression. It requires only one additional measurement of the linear current. Model accuracy was assessed by comparing to extensive SPICE delay simulations of NAND and NOR circuits designed using state-of-the-art MOS technologies. Comparison results show that $\textit {CV}_{\text {dd}}/{I}_{\text {stack}}$ equation provides ~15% accuracy for NAND/NOR circuits in line with $\textit {CV}_{\text {dd}}/{I}_{\text {eff}}$ accuracy for inverter. In an era of emphasis on low-power design, the developed model presents convenient means of exploring design space when optimizing circuit supply voltage for low-power operation.

Degree one twisting of Deligne cohomology, as a differential refinement of integral cohomology, was established in previous work. Here we consider higher degree twists. The Rham complex, hence de Rham cohomology, admits twists of any odd degree. However, in order to consider twists of integral cohomology we need a periodic version. Combining the periodic versions of both ingredients leads us to introduce a periodic form of Deligne cohomology. We demonstrate that this theory indeed admits a twist by a gerbe of any odd degree. We present the main properties of the new theory and illustrate its use with examples and computations, mainly via a corresponding twisted differential Atiyah-Hirzebruch spectral sequence., 25 pages, paragraph added to introduction, references added

We propose a new topology-preserving method for 3D image segmentation. We treat the image as a stack of 2D images so that the topological computation can be carried only within 2D in order to achieve computational efficiency. To enforce the continuity between slices, we propose a compound multi-slice representation and a compound multi-slice topological loss that incorporates rich topological information from adjacent slices. The quantitative and qualitative results show that our proposed method outperforms various strong baselines, especially for structure-related evaluation metrics.

We probe type IIA geometries with \emph{folded} semiclassical strings those encode the strong coupling dynamics associated with long operators in a class of SCFTs pertaining to spacetimes whose dimension vary from $6d$ down to $2d$. We particularly focus on folded string configurations those are extended through stack of flavor $ Dp $ ($ p=6,8 $) branes localized along the internal manifold. Considering some specific examples within the realm of $ \mathcal{N}=2 $ linear quivers, we show that the associated string spectrum exhibits a pole as the string approaches flavor D6 branes. We identify this as a \emph{fragmentation} of long operators in the dual $ \mathcal{N}=2 $ SCFTs. On the other hand, a similar analysis for $ \mathcal{N}=(1,0) $ SCFTs in $6d$ as well as $ \mathcal{N}=(0,4) $ SCFTs in $ 4d $ reveals a set of new dispersion relations at strong coupling. Based on semiclassical calculations, we set an argument that explains either of these cases., Comment: version accepted in JHEP

The problem of Isomorphism of Polynomials (IP problem) is known to be important to study the security of multivariate public key cryptosystems, one of major candidates of post-quantum cryptography, against key recovery attacks. In these years, several schemes based on the IP problem itself or its generalization have been proposed. At PQCrypto 2020, Santoso introduced a generalization of the problem of Isomorphism of Polynomials, called the problem of Blockwise Isomorphism of Polynomials (BIP problem), and proposed a new Diffie-Hellman type encryption scheme based on this problem with Circulant matrices (BIPC problem). Quite recently, Ikematsu et al. proposed an attack called the linear stack attack to recover an equivalent key of Santoso’s encryption scheme. While this attack reduced the security of the scheme, it does not contribute to solve the BIPC problem itself. In the present paper, we describe how to solve the BIPC problem directly by simplifying the BIPC problem due to the conjugation property of circulant matrices. In fact, we experimentally solved the BIPC problem with the parameter, which has 256 bit security by Santoso’s security analysis and has 72.7 bit security against the linear stack attack, by about 10 min.

For a connected reductive group $G$ over a finite field, we study automorphic vector bundles on the stack of $G$-zips. In particular, we give a formula in the general case for the space of global sections of an automorphic vector bundle in terms of the Brylinski--Kostant filtration. Moreover, we give an equivalence of categories between the category of automorphic vector bundles on the stack of $G$-zips and a category of admissible modules with actions of a zero-dimensional algebraic subgroup a Levi subgroup and monodromy operators., Comment: 33 pages

When comparing strings together, there are some issues that can come up. When you work with primitive local value types like int, float, etc., these are stored as values on the stack that have unique memory addresses from each other. When you work with class types, like String, they refer to memory locations on the heap. When you use the equality operator, ==, it looks and returns true if the reference is equal between the two items. Sometimes, when you use class types, the references can be different, so this returns a false, even if the values in the strings are identical.

Most available semantic parsing datasets, comprising of pairs of natural utterances and logical forms, were collected solely for the purpose of training and evaluation of natural language understanding systems. As a result, they do not contain any of the richness and variety of natural-occurring utterances, where humans ask about data they need or are curious about. In this work, we release SEDE, a dataset with 12,023 pairs of utterances and SQL queries collected from real usage on the Stack Exchange website. We show that these pairs contain a variety of real-world challenges which were rarely reflected so far in any other semantic parsing dataset, propose an evaluation metric based on comparison of partial query clauses that is more suitable for real-world queries, and conduct experiments with strong baselines, showing a large gap between the performance on SEDE compared to other common datasets., Comment: NLP4Prog 2021

The paper considers the topical issue of formal description of data structures. Data structures are widely used in modern object-oriented programming to solve various practical problems. The paper introduces functions for performing operations with such data structures as stack, queue, and priority queue. The conditions that these functions must satisfy are introduced as axioms. To describe the axioms, an approach based on an abstract data type, algebraic and programmatic approaches were used.

There is no formula for general t-stack sortable permutations. Thus, we attempt to study them by establishing lower and upper bounds. Permutations that avoid certain pattern sets provide natural lower bounds. This paper presents a recurrence relation that counts the number of permutations that avoid the set (23451,24351,32451,34251,42351,43251). This establishes a lower bound on 3-stack sortable permutations. Additionally, the proof generalizes to provide lower bounds for all t-stack sortable permutations.

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

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.

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.

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.

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 .