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

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

Bandit is a framework for designing sequential experiments. In each experiment, a learner selects an arm $A \in \mathcal{A}$ and obtains an observati…

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.

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…

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

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…

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…

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…

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…

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.

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 …

We study a topologically exact, negative Schwarzian unimodal map whose critical point is non-recurrent and flat. Assuming the critical order is eithe…

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

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

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

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 …

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 …

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)

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…

We treat a problem at the interface of dynamical systems and equilibrium statistical physics. It is well-known that the geometric pressure function $…

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

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…

We effect a multifractal analysis for a strongly dissipative H\'enon-like map at the first bifurcation parameter at which the uniform hyperbolicity i…

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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