Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

We introduce Codex, a GPT language model fine-tuned on publicly available code from GitHub, and study its Python code-writing capabilities. A distinct production version of Codex powers GitHub Copilot. On HumanEval, a new evaluation set we release to measure functional correctness for synthesizing programs from docstrings, our model solves 28.8% of the problems, while GPT-3 solves 0% and GPT-J solves 11.4%. Furthermore, we find that repeated sampling from the model is a surprisingly effective strategy for producing working solutions to difficult prompts. Using this method, we solve 70.2% of our problems with 100 samples per problem. Careful investigation of our model reveals its limitations, including difficulty with docstrings describing long chains of operations and with binding operations to variables. Finally, we discuss the potential broader impacts of deploying powerful code generation technologies, covering safety, security, and economics.

Evaluating Large Language Models Trained on Code

/pdf/exploration-in-deep-reinforcement-learning-a-survey-2089tysk.pdf

Exploration in Deep Reinforcement Learning: A Survey

For any at projective family ( X;L)! C such that the generic bre X is a klt Q-Fano variety and LjX Q KX , we use the techniques from the minimal model program (MMP) to modify the total family. The end product is a family such that every ber is a klt Q-Fano variety. Moreover, we can prove that the Donaldson-Futaki invariants of the appearing models decrease. When the family is a test conguration of a xed Fano variety (X; KX), this implies Tian’s conjecture: given X a Fano manifold, to test its K-(semi, poly)stability, we only need to test on the special test congurations.

https://annals.math.princeton.edu/wp-content/uploads/annals-v180-n1-p04-s.pdf

Special test configuration and K-stability of Fano varieties

Chapter Four in Geraldine Cotter's 'Transforming Tradition: Irish traditional music in Ennis Co. Clare 1950-1980.'

Practice as learning

Let X be a minuscule Schubert variety. In this paper, we associate a quiver with X and use the combinatorics of this quiver to describe all relative minimal models � : � X → X. We prove that all the morphismsare small and give a combinatorial criterion for � X to be smooth and thus a small resolution of X. We describe in this way all small resolutions of X. As another application of this description of relative minimal models, we obtain the following more intrinsic statement of the main result of Perrin, J. Algebra 294 (2005), 431-462. Let α ∈ A1(X) be an effective 1-cycle class. Then the irreducible components of the scheme Homα(p 1 ,X ) of morphisms from P 1 to X and of class α are indexed by the set: ne(α )= {β ∈ A1( � X) | β is effective and � π∗β = α} which is independent of the choice of a relative minimal model � X of X.

/pdf/small-resolutions-of-minuscule-schubert-varieties-46v8u4c2jz.pdf

Small resolutions of minuscule Schubert varieties

We study the quantum cohomology of (co)minuscule homogeneous varieties under a unified perspective. We show that three points Gromov–Witten invariants can always be interpreted as classical intersection numbers on auxiliary varieties. Our main combinatorial tools are certain quivers, in terms of which we obtain a quantum Chevalley formula and a higher quantum Poincare duality. In particular, we compute the quantum cohomology of the two exceptional minuscule homogeneous varieties.

/pdf/quantum-cohomology-of-minuscule-homogeneous-spaces-4xwa0up8l3.pdf

Quantum Cohomology of Minuscule Homogeneous Spaces

In this paper, we describe on the one hand, all relative minimal models Y of a minuscule Schubert variety X using some combinatorics on quivers and we prove that the morphism from Y to X is small (in the sense of intersection cohomology). 
On the other hand, thanks to a result of B. Totaro, any small resolution Z of a minuscule Schubert variety X has to be a relative minimal model of X. So X admits a small resolution if and only if there exists a smooth relative minimal model Y of X. We give a combinatoric criterion for Y to be smooth describing in this way all small resolutions of X. 
We also use stringy polynomials and the relative canonical model to give another way to tell when a minuscule Schubert variety admits a small resolution.

We study the quantum cohomology of quasi-minuscule and quasi-cominuscule homogeneous spaces. The product of any two Schubert cells does not involve powers of the quantum parameter higher than 2. With the help of the quantum to classical principle we give presentations of the quantum cohomology algebras. These algebras are semi-simple for adjoint non coadjoint varieties and some properties of the induced strange duality are shown.

On the quantum cohomology of adjoint varieties

For a G-variety X with an open orbit, we define its boundary ∂ X as the complement of the open orbit. The action sheaf SX is the subsheaf of the tangent sheaf made of vector fields tangent to ∂ X. We prove, for a large family of smooth spherical varieties, the vanishing of the cohomology groups Hi(X, SX) for i > 0, extending results of Bien and Brion (Compos. Math. 104:1–26, 1996). We apply these results to study the local rigidity of the smooth projective varieties with Picard number one classified in Pasquier (Math. Ann., in press).

/pdf/local-rigidity-of-quasi-regular-varieties-4kxw1yr1wr.pdf

Local rigidity of quasi-regular varieties

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Papers

Small resolutions of minuscule Schubert varieties

Quantum Cohomology of Minuscule Homogeneous Spaces

Small resolutions of minuscule Schubert varieties

On the quantum cohomology of adjoint varieties

Local rigidity of quasi-regular varieties