arXiv research

Study limits of convex domains in projective plane, proving specific results.

Sharp estimate on harmonic maps at conformal points in balls.

We construct and study a natural homeomorphism between the moduli space of polynomial cubic differentials of degree d on the complex plane and the space of projective equivalence classes of oriented convex polygons with d+3 vertices. This map arises from the construction of a complete hyperbolic affine sphere with pres…

We show that the volume entropy of the Hilbert metric on a closed convex projective surface tends to zero as the corresponding Pick differential tends to infinity. The proof is based on the theorem, due to Benoist and Hulin, that the Hilbert metric and Blaschke metric are comparable.

Classifies Calabi hypersurfaces with parallel Fubini-Pick form.

Paper proves a discrete Schwarz-Pick lemma for generalized circle packings.

We study the uniqueness of a vortex equation involving an entire function on the complex plane. As geometric applications, we show that there is a unique harmonic map $u:\mathbb{C}\rightarrow \mathbb{H}^2$ satisfying $\partial u\neq 0$ with prescribed polynomial Hopf differential; there is a unique affine spherical imm…

Transformed geometry into algebra to prove Pick's theorem efficiently.

KLT picker automates particle picking for cryo-EM, especially for low SNR images.

We discuss the local differential geometry of convex affine spheres in $\re^3$ and of minimal Lagrangian surfaces in Hermitian symmetric spaces. In each case, there is a natural metric and cubic differential holomorphic with respect to the induced conformal structure: these data come from the Blaschke metric and Pick f…

Study geometry of tetrahedra in complex hyperbolic space and Hilbert spaces.

This paper classifies hypersurfaces in n+1 with parallel Fubini-Pick form.

We discuss the question of how to pick a matrix uniformly (in an appropriate sense) at random from groups big and small. We give algorithms in some cases, and indicate interesting problems in others.

The paper studies third-order PDEs invariant under affine transformations and connects them to the Fubini-Pick invariant.

The paper extends the Discrete Schwarz-Pick Lemma to circle packings with obtuse intersections and disjoint packings.

Optimal trend-following strategy uses simple EMA, avoiding complex cherry-picked signals.

Study finds cherry-picking load shaping strategies outperforms others in reducing grid CO2 emissions.

The paper improves ODE solvers by integrating diverse information types.

Differentiable perturbed optimizers enable end-to-end learning of discrete decisions.

We present an intriguing question about lattice points in triangles where Pick's formula is "almost correct". The question has its origin in knot theory, but its statement is purely combinatorial. After more than 30 years the topological question was recently solved, but the lattice point problem is still open.

Cryo-electron microscopy (cryo-EM) studies using single particle reconstruction are extensively used to reveal structural information on macromolecular complexes. Aiming at the highest achievable resolution, state of the art electron microscopes automatically acquire thousands of high-quality micrographs. Particles are…

In this note, we prove a Schwarz-Pick type lemma for minimal maps between negatively curved Riemannian surfaces. More precisely, we prove that if $f:M \to N$ is a minimal map with bounded Jacobian between two complete negatively curved Riemann surfaces M and N whose sectional curvatures $σ_M$ and $σ_N$ satisfy $infσ_M …

Search-based methods for hard combinatorial optimization are often guided by heuristics. Tuning heuristics in various conditions and situations is often time-consuming. In this paper, we propose NeuRewriter that learns a policy to pick heuristics and rewrite the local components of the current solution to iteratively i…

We show that the Cappell-Shaneson version of Pick's theorem for simple lattice polytopes is a consequence of a general relation between characteristic numbers of virtual submanifolds dual to the characteristic classes of a stably almost complex manifold. This relation is analogous to the miraculous cancellation formula…

In this note we discuss - in what is intended to be a pedagogical fashion - FX option pricing in target zones with attainable boundaries. The boundaries must be reflecting. The no-arbitrage requirement implies that the differential (foreign minus domestic) short-rate is not deterministic. When the band is narrow, we ca…

If we pick $n$ random points uniformly in $[0,1]^d$ and connect each point to its $k-$nearest neighbors, then it is well known that there exists a giant connected component with high probability. We prove that in $[0,1]^d$ it suffices to connect every point to $c_{d,1} \log{\log{n}}$ points chosen randomly among its $…

Study analyzes 3,171 stocks to pick efficient portfolios using quantum and classical solvers.

Mass spectrometry (MS) is an important technique for chemical profiling which calculates for a sample a high dimensional histogram-like spectrum. A crucial step of MS data processing is the peak picking which selects peaks containing information about molecules with high concentrations which are of interest in an MS in…

Geometric analysis of nonlinear dynamics applied to financial time series.

Structured prediction requires searching over a combinatorial number of structures. To tackle it, we introduce SparseMAP: a new method for sparse structured inference, and its natural loss function. SparseMAP automatically selects only a few global structures: it is situated between MAP inference, which picks a single …

Selection of appropriate collective variables for enhancing sampling of molecular simulations remains an unsolved problem in computational biophysics. In particular, picking initial collective variables (CVs) is particularly challenging in higher dimensions. Which atomic coordinates or transforms there of from a list o…

We consider the problem of evaluating the quality of startup companies. This can be quite challenging due to the rarity of successful startup companies and the complexity of factors which impact such success. In this work we collect data on tens of thousands of startup companies, their performance, the backgrounds of t…

We investigate whether a robot arm can learn to pick and throw arbitrary objects into selected boxes quickly and accurately. Throwing has the potential to increase the physical reachability and picking speed of a robot arm. However, precisely throwing arbitrary objects in unstructured settings presents many challenges:…

CAP algorithm controls FCR in online selective prediction.

We derive asset pricing formula for markets with incomplete information and subjective views.

If an artificial intelligence aims to maximise risk-adjusted return, then under mild conditions it is disproportionately likely to pick an unethical strategy unless the objective function allows sufficiently for this risk. Even if the proportion $η$ of available unethical strategies is small, the probability ${p_U}$ of…

In this paper we first analyzed the inductive bias underlying the data scattered across complex free energy landscapes (FEL), and exploited it to train deep neural networks which yield reduced and clustered representation for the FEL. Our parametric method, called Information Distilling of Metastability (IDM), is end-t…

In this article, we advocate the ensemble approach for variable selection. We point out that the stochastic mechanism used to generate the variable-selection ensemble (VSE) must be picked with care. We construct a VSE using a stochastic stepwise algorithm, and compare its performance with numerous state-of-the-art algo…

A variety of methods have been proposed for interpreting nodes in deep neural networks, which typically involve scoring nodes at lower layers with respect to their effects on the output of higher-layer nodes (where lower and higher layers are closer to the input and output layers, respectively). However, we may be inte…

New method finds significant high-order interactions efficiently.

The paper solves circle packings on surfaces with boundaries.

LTP learns per-layer thresholds for efficient pruning of deep networks.

This paper introduces a novel, well-founded, betweenness measure, called the Bag-of-Paths (BoP) betweenness, as well as its extension, the BoP group betweenness, to tackle semisupervised classification problems on weighted directed graphs. The objective of semi-supervised classification is to assign a label to unlabele…

Cryo-electron microscopy (cryoEM) is an increasingly popular method for protein structure determination. However, identifying a sufficient number of particles for analysis (often >100,000) can take months of manual effort. Current computational approaches are limited by high false positive rates and require significant…

We consider a two-person trading game in continuous time whereby each player chooses a constant rebalancing rule $b$ that he must adhere to over $[0,t]$. If $V_t(b)$ denotes the final wealth of the rebalancing rule $b$, then Player 1 (the `numerator player') picks $b$ so as to maximize $\mathbb{E}[V_t(b)/V_t(c)]$, whil…

We study fibrations $\cV$ of toric varieties over the flag variety $G/T$, where $G$ is a compact semisimple Lie group and $T$ is a maximal torus. From symplectic data, we construct test configurations of $\cV$ and compute their Futaki invariants by employing a generalization of Pick's Theorem. We also give a simple for…

We pick up the regime switching model for asset returns introduced by Rogers and Zhang. The calibration involves various markets including implied volatility in order to gain additional predictive power. We focus on the calculation of risk measures by Fourier methods that have successfully been applied to option pricin…

Deep neural networks (DNNs) have been widely used in the fields such as natural language processing, computer vision and image recognition. But several studies have been shown that deep neural networks can be easily fooled by artificial examples with some perturbations, which are widely known as adversarial examples. A…