arXiv research

We show numerically that any of the constant mean curvature tori first found by Wente must have index at least eight.

Constructs surfaces with conical singularities using variational methods.

Paper extends Wente's result to anisotropic capillary surfaces in half-spaces.

Isothermic tori with one planar curvature line found and characterized.

We find various lower and upper bounds for the index of Wente tori that contain a continuous family of planar principal curves. We then prove a result that gives an algorithm for computing the index sharply.

Study constant mean curvature tori in R^3 using spectral data and Whitham deformations.

Biotech IPOs in Q1 2021: advanced degrees, clinical trials, and IP key.

We study the geometry and topology of immersed surfaces in Euclidean 3-space whose Gauss map satisfies a certain two-piece-property, and solve the ``shadow problem" formulated by H. Wente.

Using the functional associated with the optimal Wente inequality for pairs of functions on 2-dimensional domains, we show the existence of solutions to the H-system on an annulus satisfying Neumann boundary conditions.

We study almost complex surfaces in the nearly Kähler $S^3\times S^3$. We show that there is a local correspondence between almost complex surfaces and solutions of the H-surface equation introduced by Wente. We find a global holomorphic differential on every almost complex surface, and show that when this differentia…

The classical Liouville theorem states that a bounded harmonic function on all of $\RR^n$ must be constant. In the early 1970s, S.T. Yau vastly generalized this, showing that it holds for manifolds with nonnegative Ricci curvature. Moreover, he conjectured a stronger Liouville property that has generated many significa…

New minimal surfaces found with spherical curvature lines.

We consider embedded ring-type surfaces (that is, compact, connected, orientable surfaces with two boundary components and Euler-Poincaré characteristic zero) in ${\bold R}^3$ of constant mean curvature which meet planes $Π_1$ and $Π_2$ in constant contact angles $γ_1$ and $γ_2$ and bound, together with those planes, a…

In [1], Connes presented axioms governing noncommutative geometry. He went on to claim that when specialised to the commutative case, these axioms recover spin or spin^c geometry depending on whether the geometry is ''real'' or not. We attempt to flesh out the details of Connes' ideas. As an illustration we present a p…

In this paper almost complex surfaces of the nearly Kähler $S^3\times S^3$ are studied in a systematic way. We show that on such a surface it is possible to define a global holomorphic differential, which is induced by an almost product structure on the nearly Kähler $S^3\times S^3$. We also find a correspondence betwe…

In the present work we establish a quantization result for the angular part of the energy of solu- tions to elliptic linear systems of Schrödinger type with antisymmetric potentials in two dimension. This quantization is a consequence of uniform Lorentz-Wente type estimates in degenerating annuli. We derive from this a…

We use the 2-loop term of the Kontsevich integral to show that there are (many) knots with trivial Alexander polynomial which don't have a Seifert surface whose genus equals the rank of the Seifert form. This is one of the first applications of the Kontsevich integral to intrinsically 3-dimensional questions in topolog…

On December 16, Zynga, the well-known social game developing company went public. This event is following other recent IPOs in the world of social networking companies, such as Groupon, Linkedin or Pandora to cite a few. With a valuation close to 7 billion USD at the time when it went public, Zynga has become the bigge…

New examples show non-rotational annuli in a ball, solving a uniqueness problem.

This paper investigates the common intuition suggesting that during crises the shape of the financial market clearly differentiates from that of random walk processes. In this sense, it challenges the analysis of the nature of financial markets proposed by Fama and his associates. For this, a geometric approach is prop…

Partial differential equations (PDEs) are widely used across the physical and computational sciences. Decades of research and engineering went into designing fast iterative solution methods. Existing solvers are general purpose, but may be sub-optimal for specific classes of problems. In contrast to existing hand-craft…

This article presents a preliminary approach towards characterizing political fake news on Twitter through the analysis of their meta-data. In particular, we focus on more than 1.5M tweets collected on the day of the election of Donald Trump as 45th president of the United States of America. We use the meta-data embedd…

On December 16th, 2011, Zynga, the well-known social game developing company went public. This event followed other recent IPOs in the world of social networking companies, such as Groupon or Linkedin among others. With a valuation close to 7 billion USD at the time when it went public, Zynga became one of the biggest …

Human reasoning involves recognising common underlying principles across many examples. The by-products of such reasoning are invariants that capture patterns such as "if someone went somewhere then they are there", expressed using variables "someone" and "somewhere" instead of mentioning specific people or places. Hum…

New minimal annuli found in unit ball, solving old problems.

FIT evaluates time series model feature importance quantifying distributional shift.

We introduce a method by which a generative model learning the joint distribution between actions and future states can be used to automatically infer a control scheme for any desired reward function, which may be altered on the fly without retraining the model. In this method, the problem of action selection is reduce…

We study closed smooth convex plane curves $Γ$ enjoying the following property: a pair of points $x,y$ can traverse $Γ$ so that the distances between $x$ and $y$ along the curve and in the ambient plane do not change; such curves are called {\it bicycle curves}. Motivation for this study comes from the problem how to d…

The topological properties of interbank networks have been discussed widely in the literature mainly because of their relevance for systemic risk. Here we propose to use the Stochastic Block Model to investigate and perform a model selection among several possible two block organizations of the network: these include b…

In accordance with "Democracy's Effect on Development: More Questions than Answers", we seek to carry out a study in following the description in the 'Questions for Further Study.' To that end, we studied 33 countries in the Sub-Saharan Africa region, who all went through an election which should signal a "step-up" for…

The principle of peer review is central to the evaluation of research, by ensuring that only high-quality items are funded or published. But peer review has also received criticism, as the selection of reviewers may introduce biases in the system. In 2014, the organizers of the ``Neural Information Processing Systems\r…

Measures policy-violating content prevalence with ML-assisted sampling and LLM labeling.

Since the beginning of the new millennium, stock markets went through every state from long-time troughs, trade suspensions to all-time highs. The literature on asset pricing hence assumes random processes to be underlying the movement of stock returns. Observed procyclicality and time-varying correlation of stock retu…

Study on multitask learning performance factors.

Neural network predicts vessel motions with high accuracy.

This thesis was concerned with classifying the real indecomposable solvable Lie algebras with codimension one nilradicals of dimensions two through seven. This thesis was organized into three chapters. In the first, we described the necessary concepts and definitions about Lie algebras as well as a few helpful theorems…

What would you do if you were invited to play a game where you were given \$25 and allowed to place bets for 30 minutes on a coin that you were told was biased to come up heads 60% of the time? This is exactly what we did, gathering 61 young, quantitatively trained men and women to play this game. The results, in a nut…

Establishes interior regularity results for a broad class of two-dimensional nonlinear elliptic systems using a unified abstract framework.

A remarkable similarity in the behavior of the US S&P500 index from 1996 to August 2002 and of the Japanese Nikkei index from 1985 to 1992 (11 years shift) is presented, with particular emphasis on the structure of the bearish phases. Extending a previous analysis of Johansen and Sornette [1999, 2000] on the Nikkei ind…

Study finds billing codes at IPO boost digital health companies' financial performance.

Fermat constants fail to fully identify Clairaut constants for certain geodesics on a surface of revolution.

Study proves surfaces with constant curvature are simple shapes.

Machine learning analyzed peer reviews to find differences in quality by journal impact factor.

The paper classifies hypersurfaces in $\mathbb{H}^2 imes\mathbb{H}^2$ with constant curvature.

Study on biconservative hypersurfaces with constant scalar curvature in space forms.

We prove several facts about the Yamabe constant of Riemannian metrics on general noncompact manifolds and about S. Kim's closely related "Yamabe constant at infinity". In particular we show that the Yamabe constant depends continuously on the Riemannian metric with respect to the fine C^2-topology, and that the Yamabe…

Study CR Yamabe constant and CR structures on manifolds.

The paper studies curves of constant-ratio in pseudo-Galilean space.