arXiv research

Singapore's cooling measures did not increase housing wealth overall.

Estimates Bartnik mass for metrics with nonnegative Gauss curvature.

New predictive bandit model with noise for better decision making.

FedCM measures contributions in real-time for federated learning.

Efficient methods reduce projections in non-stationary online learning.

We develop a novel stress-test framework to monitor systemic risk in financial systems. The modular structure of the framework allows to accommodate for a variety of shock scenarios, methods to estimate interbank exposures and mechanisms of distress propagation. The main features are as follows. First, the framework al…

The entropy of a hypersurface is a geometric invariant that measures complexity and is invariant under rigid motions and dilations. It is given by the supremum over all Gaussian integrals with varying centers and scales. It is monotone under mean curvature flow, thus giving a Lyapunov functional. Therefore, the entropy…

New ANN method for imputing rounded zeros in compositional data.

The paper applies thermodynamics to financial markets to prove no-arbitrage constraints.

A framework for collaborative learning reduces communication rounds.

Gradient descent with biased rounding errors converges faster under certain conditions.

The paper examines stability of the Sobolev inequality in metric spaces with curvature dimension conditions.

Round surgery diagrams represent 3-manifolds in $S^3$.

We prove a Chern-Lashof type formula computing the expected number of critical points of smooth function on a smooth manifold $M$ randomly chosen from a finite dimensional subspace $V\subset C^\infty(M)$ equipped with a Gaussian probability measure. We then use this formula this formula to find the asymptotics of the e…

Contact round surgeries on $(\mathbb{S}^3,ξ_{st})$ help in constructing and understanding contact 3-manifolds.

In this article, we extend Huisken's theorem that convex surfaces flow to round points by mean curvature flow. We construct certain classes of mean convex and non-mean convex hypersurfaces that shrink to round points and use these constructions to create pathological examples of flows. We find a sequence of flows that …

Optimizes sample and round complexity in adaptive sampling from multiple distributions.

The paper proposes a conjecture for a symmetric version of Ehrhard's inequality.

Study non-local isoperimetric energies on spheres using a Riemannian autocorrelation function.

Consider an analytic map of a neighborhood of 0 in a vector space to a Euclidean space. Suppose that this map takes all germs of lines passing through 0 to germs of circles. Such a map is called rounding. We introduce a natural equivalence relation on roundings and prove that any rounding, whose differential at 0 has r…

New findings show infinitely many knots cannot be smoothly round handle slices.

We discuss the integrability of orthogonal almost complex structures on Riemannian products of even-dimensional round spheres and give a partial answer to the question raised by E. Calabi concerning the existence of complex structures on a product manifold of a round 2-sphere and a round 4-sphere.

Algorithm minimizes regret while adhering to unknown safety constraints.

This work investigates how multi-round reasoning improves LLM performance.

New findings on $κ$-solutions with round cylinder as asymptotic shrinker.

Round balls minimize liquid drop model volumes ≤ 1.

Gradient descent stagnates in low-precision, but unbiased rounding schemes improve convergence.

Round cylinders are rigid in Ricci shrinkers close to the standard product.

In this paper we study the limitations of parallelization in convex optimization. A convenient approach to study parallelization is through the prism of \emph{adaptivity} which is an information theoretic measure of the parallel runtime of an algorithm [BS18]. Informally, adaptivity is the number of sequential rounds a…

A half-geodesic is a closed geodesic realizing the distance between any pair of its points. All geodesics in a round sphere are half-geodesics. Conversely, this note establishes that Riemannian spheres with all geodesics closed and sufficiently many half-geodesics are round.

We show that if the entropy of any closed hypersurface is close to that of a round hyper-sphere, then it is close to a round sphere in Hausdorff distance. Generalizing the result of \cite{BW1} to higher dimensions.

In this paper, we study the limiting behavior of the Brown-York mass and Hawking mass along nearly round surfaces at infinity of an asymptotically flat manifold. Nearly round surfaces can be defined in an intrinsic way. Our results show that the ADM mass of an asymptotically flat 3-manifold can be approximated by some …

We introduce a minorization-maximization approach to optimizing common measures of discovery significance in high energy physics. The approach alternates between solving a weighted binary classification problem and updating class weights in a simple, closed-form manner. Moreover, an argument based on convex duality sho…

The study characterizes round spheres in Euclidean space based on r-mean curvature conditions.

Study non-stationary online auctions with semi-bandit feedback.

Contact round surgery of contact 3-manifolds is introduced in this paper. By using this method, an alternative proof of the existence of a contact structure on any closed orientable 3-manifold is given. It is also proved that any contact structure on any closed orientable 3-manifold is constructed from the standard con…

In recent work, the notion of Double Convexity for a foliation of a conical null hypersurface was introduced to give a proof, if satisfied, of the Null Penrose Inequality. Double Convexity constrains the geometry of a Marginally Outer Trapped Surface (MOTS), called a quasi-round MOTS. In the first part of this paper, f…

New efficient algorithm for approximate PML distribution.

Study cohomology rings of 3D manifolds with round fold maps into the plane.

Research explores real algebraic realization of round fold maps of codimension -1.

New compact mean convex hypersurfaces found for positive λ.

New Einstein metrics found on a 10-dimensional sphere.

We classify the radially symmetric connections in vector bundles over round spheres by proving that they are all parallel.

We present the Round Handle Problem, proposed by Freedman and Krushkal. It asks whether a collection of links, which contains the Generalised Borromean Rings, are slice in a 4-manifold R constructed from adding round handles to the four ball. A negative answer would contradict the union of the surgery conjecture and th…

We prove that the well-rounded retract of SO_n\SL_n(R) is a minimal SL_n(Z)-invariant spine.

High-frequency traders can act as either small informed traders or round-trippers, affecting price discovery and liquidity.

One-round FL method improves robustness and reduces communication rounds.

Eigenvalues on spheres are compared to the unit round sphere, proving a sharp bound and equality condition.