arXiv research

Existence proved for complex 3-folds equation on a specific phase range.

In this paper we construct Mabuchi $\mathcal{L}^{\rm M}_ω$ functional and Aubin-Yau functionals $\mathcal{I}^{\rm AY}_ω, \mathcal{J}^{\rm AY}_ω$ on any compact complex three-folds. The method presented here will be used in the forthcoming paper \cite{L1} on the construction of those functionals on any compact complex m…

In the previous papers \cite{L1, L2} the author constructed Mabuchi and Aubin-Yau functionals over any complex surfaces and three-folds, respectively. Using the method in \cite{L2}, we construct those functionals over any complex manifolds of the complex dimension bigger than or equal to 2.

Paper proves structure of compact Kähler 3-folds with specific bundles.

We develop numerical algorithms for solving the Einstein equation on Calabi-Yau manifolds at arbitrary values of their complex structure and Kahler parameters. We show that Kahler geometry can be exploited for significant gains in computational efficiency. As a proof of principle, we apply our methods to a one-paramete…

Deligne and Mostow constructed a class of lattices in PU(2,1) using monodromy of hypergeometric functions. Later, Thurston reinterpreted them in terms of cone metrics on the sphere. In this spirit we construct a fundamental domain for all lattices with three fold symmetry in Deligne-Mostow list. This is a generalisatio…

We consider a generalised complex Monge-Ampère equation on a compact Kähler manifold and treat it using the method of continuity. For complex surfaces, we prove an easy existence result. We also prove that (for three-folds and a related real PDE in a ball), as long as the Hessian is bounded below by a pre-determined co…

Calculates Laplacian spectra on Calabi-Yau hypersurfaces.

The moduli space of the Calabi-Yau three-folds, which play a role as superstring ground states, exhibits the same {\em special geometry} that is known from nonlinear sigma models in $N=2$ supergravity theories. We discuss the symmetry structure of special real, complex and quaternionic spaces. Maps between these spaces…

For any alternating knot, it is known that the double branched cover of the $3$-sphere branched over the knot is an $L$-space. We show that the three-fold cyclic branched cover is also an $L$-space for any genus one alternating knot.

Study on positivity properties of vector bundle Monge-Ampère equation.

We describe an action of $U(1)\times Sp(1)$ on $HP^7$ that allows to obtain a $Z_2$-quotient of CAYLEY (the Grassmannian of oriented 4-planes in $R^8$ closed under the three-fold cross product) by quaternionic Kähler reduction.

Let $X$ be a complex four-dimensional compact Calabi-Yau manifold equipped with a Kähler form $ω$ and a holomorphic four-form $Ω$. Under certain assumptions, we define Donaldson-Thomas type deformation invariants by studying the moduli space of the solutions of Donaldson-Thomas equations on the given Calabi-Yau manifol…

MNIST-NET10 fusion improves MNIST classification to 0.1% error rate.

New $G_2$-holonomy manifolds from 5d N=1 theories domain walls.

We consider Bridgeland stability conditions for three-folds conjectured by Bayer-Macrì-Toda in the case of Picard rank one. We study the differential geometry of numerical walls, characterizing when they are bounded, discussing possible intersections, and showing that they are essentially regular. Next, we prove that w…

We define a notion of stability for chiral ring of four dimensional N=1 theory by introducing test chiral rings and generalized a maximization. We conjecture that a chiral ring is the chiral ring of a superconformal field theory if and only if it is stable. We then study N=1 field theory derived from D3 branes probing …

This paper simplifies OPE in large state spaces using state abstractions.

Constructs explicit nontrivial cycles in Habiro cohomology of smooth varieties.

In today's increasingly international economy, return and volatility spillover effects across international equity markets are major macroeconomic drivers of stock dynamics. Thus, information regarding foreign markets is one of the most important factors in forecasting domestic stock prices. However, the cross-correlat…

4-manifolds with specific trisections are 3-fold covers of S^4.

We demonstrate the equivalence of all loop closed topological string amplitudes on toric local Calabi-Yau threefolds with computations of certain knot invariants for Chern-Simons theory. We use this equivalence to compute the topological string amplitudes in certain cases to very high degree and to all genera. In parti…

Deformed holomorphic Chern-Simons theory yields new instantons.

We review aspects of twistor theory, its aims and achievements spanning thelast five decades. In the twistor approach, space--time is secondary with events being derived objects that correspond to compact holomorphic curves in a complex three--fold -- the twistor space. After giving an elementary construction of this s…

Null Kähler metrics are characterized by Painlevé I or II ODEs.

Minkowski space is the local model of 3 dimensionnal flat spacetimes. Recent progress in the description of globally hyperbolic flat spacetimes showed strong link between Lorentzian geometry and Teichm{ü}ller space. We notice that Lorentzian generalisations of conical singularities are useful for the endeavours of desc…

Iterative Hessian sketch (IHS) is an effective sketching method for modeling large-scale data. It was originally proposed by Pilanci and Wainwright (2016; JMLR) based on randomized sketching matrices. However, it is computationally intensive due to the iterative sketch process. In this paper, we analyze the IHS algorit…

Study links public concern in Italy to financial markets worldwide.

New explicit constructions of unbalanced Ramanujan bipartite graphs.

An irreducible representation of the free group on two generators X,Y into SL(2,C) is determined up to conjugation by the traces of X,Y and XY. We study the diagonal slice of representations for which X,Y and XY have equal trace. Using the three-fold symmetry and Keen-Series pleating rays we locate those groups which a…

We examine a class of deep learning models with a tractable method to compute information-theoretic quantities. Our contributions are three-fold: (i) We show how entropies and mutual informations can be derived from heuristic statistical physics methods, under the assumption that weight matrices are independent and ort…

We study the duality between M-theory on compact holonomy G2-manifolds and the heterotic string on Calabi-Yau three-folds. The duality is studied for K3-fibered G2-manifolds, called twisted connected sums, which lend themselves to an application of fiber-wise M-theory/Heterotic Duality. For a large class of such G2-man…

Single-layer GCN model improves recommendation performance with less complexity.

M-theory on compact eight-manifolds with $\mathrm{Spin}(7)$-holonomy is a framework for geometric engineering of 3d $\mathcal{N}=1$ gauge theories coupled to gravity. We propose a new construction of such $\mathrm{Spin}(7)$-manifolds, based on a generalized connected sum, where the building blocks are a Calabi-Yau four…

New model improves histopathology classification across magnifications.

Existing ordinal embedding methods usually follow a two-stage routine: outlier detection is first employed to pick out the inconsistent comparisons; then an embedding is learned from the clean data. However, learning in a multi-stage manner is well-known to suffer from sub-optimal solutions. In this paper, we propose a…

High-dimensional regression models struggle with resampling methods.

Discusses handling intercurrent events in clinical trials with time-to-event outcomes.

Method for conditional sampling with pre-trained normalizing flows.

Paper proposes a new method for efficient hyperparameter optimization.

New method makes CNN interpretations robust to adversarial attacks.

Count data are often used in recommender systems: they are widespread (song play counts, product purchases, clicks on web pages) and can reveal user preference without any explicit rating from the user. Such data are known to be sparse, over-dispersed and bursty, which makes their direct use in recommender systems chal…

Generative Adversarial Networks (GANs) have seen steep ascension to the peak of ML research zeitgeist in recent years. Mostly catalyzed by its success in the domain of image generation, the technique has seen wide range of adoption in a variety of other problem domains. Although GANs have had a lot of success in produc…

A new method for efficient optimization of expensive simulations on HPC.

Most practical recommender systems focus on estimating immediate user engagement without considering the long-term effects of recommendations on user behavior. Reinforcement learning (RL) methods offer the potential to optimize recommendations for long-term user engagement. However, since users are often presented with…

Paper proposes an adversarial sampling method for efficient extreme classification.

With the rapid development of social media sharing, people often need to manage the growing volume of multimedia data such as large scale video classification and annotation, especially to organize those videos containing human activities. Recently, manifold regularized semi-supervised learning (SSL), which explores th…

The integrability of the geodesic flow on the three-folds $\mathcal M^3$ admitting $SL(2,\mathbb R)$-geometry in Thurston's sense is investigated. The main examples are the quotients $\mathcal M^3_Γ=Γ\backslash PSL(2,\mathbb R)$, where $Γ\subset PSL(2,\mathbb R)$ is a cofinite Fuchsian group. We show that the correspon…