arXiv research

Study nondegenerate singularities in mean curvature flow.

We show several results comparing sharp eigenvalue bounds for the first Steklov eigenvalue on surfaces under change of the topology. Among others, we obtain strict monotonicity in the genus. Combined with results of the second named author \cite{petrides_2} this implies the existence of free boundary minimal immersions…

New surgery operation preserves monotonicity of Lagrangians.

Paper finds how Steklov eigenvalues change on graphs and trees.

We derive a monotonicity formula and classify finite Morse index solutions (positive or sign-changing, radial or not) to the following triharmonic Lane-Emden equation: \begin{equation}\nonumber (-Δ)^3 u=|u|^{p-1}u \hbox{ in } \mathbb{R}^n, \end{equation} where $p$ is below the Joseph-Lundgren exponent. As a byproduct w…

This paper benchmarks monotone-constrained models for credit PD across datasets and finds constraints are mostly costless.

Derives a new formula for optimal stopping problems with exploding derivatives.

Using the stress energy tensor, we establish some monotonicity formulae for vector bundle-valued p-forms satisfying the conservation law, provided that the base Riemannian (resp. Kähler) manifolds poss some real (resp. complex) p-exhaustion functions. Vanishing theorems follow immediately from the monotonicity formulae…

It has been noticed that some external CVIs exhibit a preferential bias towards a larger or smaller number of clusters which is monotonic (directly or inversely) in the number of clusters in candidate partitions. This type of bias is caused by the functional form of the CVI model. For example, the popular Rand index (R…

In this paper, we describe a newly discovered statistical property of time series data for daily price changes. We conducted quantitative investigation of the {\it calm-time intervals} of price changes for 800 companies listed in the Tokyo Stock Exchange, and for the Nikkei 225 index over a 27-year period from January …

In foreign exchange markets monotonic rate changes can be observed in time scale of order of an hour on the days that governmental interventions took place. We estimate the starting time of an intervention using this characteristic behavior of the exchange rates. We find that big amount of interventions can shift the a…

The paper examines how the first Steklov-Dirichlet eigenvalue changes with the distance between two concentric circles.

Recent reports have described that the equivalent sample size (ESS) in a Dirichlet prior plays an important role in learning Bayesian networks. This paper provides an asymptotic analysis of the marginal likelihood score for a Bayesian network. Results show that the ratio of the ESS and sample size determine the penalty…

We investigate possible origins of trends using a deterministic threshold model, where we refer to long-term variabilities of price changes (price movements) in financial markets as trends. From the investigation we find two phenomena. One is that the trend of monotonic increase and decrease can be generated by dealers…

New method makes CP intervals locally adaptive using trainable transformations.

TDX predicts evolving distributions from streaming data.

The paper extends the avoidance principle for mean curvature flows, proving new intersection dimension monotonicity results.

The paper studies how the first eigenvalue of a weighted p-Laplacian changes over time on Riemannian manifolds.

Investigates how trading boundaries change with transaction costs in portfolio selection.

Identifying changes in model parameters is fundamental in machine learning and statistics. However, standard changepoint models are limited in expressiveness, often addressing unidimensional problems and assuming instantaneous changes. We introduce change surfaces as a multidimensional and highly expressive generalizat…

We consider Liouville-type and partial regularity results for the nonlinear fourth-order problem $$ Δ^2 u=|u|^{p-1}u\ \{in} \ \R^n,$$ where $p>1$ and $n\ge1$. We give a complete classification of stable and finite Morse index solutions (whether positive or sign changing), in the full exponent range. We also compute an…

In this paper we apply change of numeraire techniques to the optimal transport approach for computing model-free prices of derivatives in a two periods model. In particular, we consider the optimal transport plan constructed in \cite{HobsonKlimmek2013} as well as the one introduced in \cite{BeiglJuil} and further studi…

For an oriented knot diagram D, the warping degree d(D) is the smallest number of crossing changes which are needed to obtain the monotone diagram from D in the usual way. We show that d(D) + d(-D) + 1 is less than or equal to the crossing number of D. Moreover the equality holds if and only if D is an alternating diag…

We simplify neural networks to 3D to study their topological changes.

Optimizes decisions under strategic individual behavior.

This paper considers a cross-layer adaptive modulation system that is modeled as a Markov decision process (MDP). We study how to utilize the monotonicity of the optimal transmission policy to relieve the computational complexity of dynamic programming (DP). In this system, a scheduler controls the bit rate of the m-qu…

This paper finds all prime alternating knots with minimal warping degree two.

The paper addresses monotonicity in machine learning models for fairness and accountability.

A new method for disentangled latent spaces in VAEs that can manipulate attributes.

We consider the problem of optimal portfolio selection under forward investment performance criteria in an incomplete market. The dynamics of the prices of the traded assets depend on a pair of stochastic factors, namely, a slow factor (e.g. a macroeconomic indicator) and a fast factor (e.g. stochastic volatility). We …

Bayesian ARMA model with directional shifts captures structural breaks in compositional time series.

The paper tackles non-monotonic learning performance and proposes algorithms to make models more monotone.

Probit Monotone BART estimates binary outcomes using monotonic functions.

In this note, we study Liouville type theorem for conformal Gaussian curvature equation (also called the mean field equation) $-Δu=K(x)e^u, in R^2$ where $K(x)$ is a smooth function on $R^2$. When $K(x)=K(x_1)$ is a sign-changing smooth function in the real line $R$, we have a non-existence result for the finite to…

Monotone neural networks can approximate and interpolate functions efficiently.

Improves k-NN for monotonic data with robustness against noise.

TRACE analyzes risk changes in models trained on shifted data.

Study examines explainable machine learning for monotonic models, finding Integrated gradients better for strong monotonicity.

Formula proves monotonicity for anisotropic minimal hypersurfaces.

New algorithm for maximizing submodular functions in real-time data changes.

The paper develops algorithms to restore monotonicity in non-monotone functions.

New example of manifolds with monotonic heat kernels found.

Proposes a Bayesian nonparametric model for monotonic functions.

Nonnegative matrix factorization (NMF) factorizes a non-negative matrix into product of two non-negative matrices, namely a signal matrix and a mixing matrix. NMF suffers from the scale and ordering ambiguities. Often, the source signals can be monotonous in nature. For example, in source separation problem, the source…

In [S. Basu, A. Gabrielov, N. Vorobjov, Semi-monotone sets. arXiv:1004.5047v2 (2011)] we defined semi-monotone sets, as open bounded sets, definable in an o-minimal structure over the reals, and having connected intersections with all translated coordinate cones in R^n. In this paper we develop this theory further by d…

COMET learns monotonic neural networks by incorporating counterexamples.

Monotonic differentiable sorting networks improve upon previous methods.

We prove three new monotonicity formulas for manifolds with a lower Ricci curvature bound and show that they are connected to rate of convergence to tangent cones. In fact, we show that the derivative of each of these three monotone quantities is bounded from below in terms of the Gromov-Hausdorff distance to the neare…