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Feb 10, 2017
Risk Management
Statistics Theory
Computational Finance

Estimation of Risk Contributions with MCMC

Determining risk contributions by unit exposures to portfolio-wide economic capital is an important task in financial risk management. Despite its pr…
Sep 05, 2017
Machine Learning

Boosting the kernelized shapelets: Theory and algorithms for local …

We consider binary classification problems using local features of objects. One of motivating applications is time-series classification, where featu…
Jun 06, 2018
Machine Learning

Causal Bandits with Propagating Inference

Bandit is a framework for designing sequential experiments. In each experiment, a learner selects an arm $A \in \mathcal{A}$ and obtains an observati…
May 07, 2007
Differential Geometry
Analysis of PDEs

In this section we use WCS classes to distinguish different S1 actions on M=S2×S3. We use this to conclude that π1(Diff(M),id) is infinite.

Secondary Characteristic Classes on Loop Spaces

A Riemannian metric on a manifold M induces a family of Riemannian metrics on the loop space LM depending on a Sobolev space parameter s. The connect…
Dec 27, 2014
Dynamical Systems

Equilibrium measures at temperature zero for Hénon-like maps at the …

We develop a thermodynamic formalism for a strongly dissipative H\'enon-like map at the first bifurcation parameter at which the uniform hyperbolicit…
Jul 09, 2014
Differential Geometry

In this section we produce several infinite families of nonhomeomorphic 5-manifolds ¯¯¯¯¯¯M with π1(Diff(¯¯¯¯¯¯M))=π1(Diff(¯¯¯¯¯¯M),Id) infinite. These manifolds are the total space of circle bundles over integral Kähler surfaces. To give some conte…

The Geometry of Loop Spaces II: Characteristic Classes

Using the Wodzicki residue, we build Wodzicki-Chern-Simons (WCS) classes in $H^{2k-1}(LM)$ associated to the residue Chern character on the loop spac…
Sep 09, 2014
Dynamical Systems

Distribution of Patches in Tilings and Spectral Properties of Corre…

A tiling is a cover of R^d by tiles such as polygons that overlap only on their borders. A patch is a configuration consisting of finitely many tiles…
Jan 20, 2021
Machine Learning

Near-Optimal Regret Bounds for Contextual Combinatorial Semi-Bandits …

The contextual combinatorial semi-bandit problem with linear payoff functions is a decision-making problem in which a learner chooses a set of arms w…
May 16, 2014
Differential Geometry

In this section, we relate our work to Freed’s work on based loop groups ΩG [3]. We find a particular representation of the loop algebra that controls the order of the curvature of the H1 metric on ΩG.

The Geometry of Loop Spaces I: $H^s$-Riemannian Metrics

A Riemannian metric on a manifold M induces a family of Riemannian metrics on the loop space LM depending on a Sobolev space parameter s. We compute …
Aug 12, 2017
Dynamical Systems
Probability

Large Deviation Principle for $S$-unimodal maps with flat critical po…

We study a topologically exact, negative Schwarzian unimodal map whose critical point is non-recurrent and flat. Assuming the critical order is eithe…
Feb 13, 2020
Data Structures and Algorithms
Machine Learning

In this section, we present algorithms for a cardinality constraint and a matroid constraint, respectively.

Approximability of Monotone Submodular Function Maximization under …

Maximizing a monotone submodular function under various constraints is a classical and intensively studied problem. However, in the single-pass strea…
Jan 14, 2014
Statistics Theory

Empirical geodesic graphs and CAT(k) metrics for data analysis

A methodology is developed for data analysis based on empirically constructed geodesic metric spaces. For a probability distribution, the length alon…
Mar 26, 2018
Dynamical Systems

Boundary of the horseshoe locus for the Hénon family

The purpose of this article is to investigate geometric properties of the parameter locus of the H\'enon family where the uniform hyperbolicity of a …
Jan 08, 2010

Unruh Effect and Holography

We study the Unruh effect on the dynamics of quarks and mesons in the context of AdS$_5$/CFT$_4$ correspondence. We adopt an AdS$_5$ metric with the …
Mar 25, 2015
Differential Geometry

In this section, we study the geometry of (R3,d∞0), and conclude that there are no isometry between (R3,d∞0) and (R3,h0), and between (R3,d∞0) and (R3,1|ζ|h0)

The nonuniqueness of the tangent cones at infinity of Ricci-flat ma…

It is shown by Colding and Minicozzi the uniqueness of the tangent cone at infinity of Ricci-flat manifolds with Euclidean volume growth which has at…
Mar 02, 2016
Dynamical Systems
Mathematical Physics

Removal of phase transition of the Chebyshev quadratic and thermody…

We treat a problem at the interface of dynamical systems and equilibrium statistical physics. It is well-known that the geometric pressure function $…
Mar 07, 2019
Geometric Topology
Symplectic Geometry

Unchaining surgery and topology of symplectic 4-manifolds

We study a symplectic surgery operation we call unchaining, which effectively reduces the second Betti number and the symplectic Kodaira dimension at…
Nov 20, 2018
Machine Learning

Multiple-Instance Learning by Boosting Infinitely Many Shapelet-based…

We propose a new formulation of Multiple-Instance Learning (MIL). In typical MIL settings, a unit of data is given as a set of instances called a bag…
Jan 31, 2015
Dynamical Systems

Birkhoff spectrum for Hénon-like maps at the first bifurcation

We effect a multifractal analysis for a strongly dissipative H\'enon-like map at the first bifurcation parameter at which the uniform hyperbolicity i…
Aug 07, 2017
Metric Geometry
Combinatorics

Discrete Midpoint Convexity

For a function defined on a convex set in a Euclidean space, midpoint convexity is the property requiring that the value of the function at the midpo…
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