The study examines different types of equilibria for stopping problems in one-dimensional diffusion processes.
problem Characterizing and comparing different types of equilibria for time-inconsistent stopping problems.
method Analyzes log sub-additive discount functions and one-dimensional diffusion processes to derive necessary and sufficient conditions for weak equilibria and other types of equilibria.
result Conditions for weak equilibria and their implications for other types of equilibria are provided.
A new class of risk measures called cash sub-additive risk measures is introduced to assess the risk of future financial, nonfinancial and insurance positions. The debated cash additive axiom is relaxed into the cash sub additive axiom to preserve the original difference between the numeraire of the current reserve amo…
The paper establishes a sub-additive inequality for volume and ε-phase-transition spectra of Riemannian manifolds.
problem Analyzing the volume and ε-phase-transition spectra of Riemannian manifolds.
method Using the Almgren-Pitts width and Allen-Cahn approach.
result Proves sub-additive inequalities for volume and ε-phase-transition spectra.
Study optimal stopping times for multi-dimensional processes with non-exponential discounting.
problem Optimal stopping in multi-dimensional processes with non-exponential discounting.
method Probabilistic potential theory to establish existence of optimal equilibria.
result Existence of optimal equilibria for multi-dimensional stopping problems.
A \emph{new} notion of equilibrium, which we call \emph{strong equilibrium}, is introduced for time-inconsistent stopping problems in continuous time. Compared to the existing notions introduced in ArXiv: 1502.03998 and ArXiv: 1709.05181, which in this paper are called \emph{mild equilibrium} and \emph{weak equilibrium…
For an infinite-horizon continuous-time optimal stopping problem under non-exponential discounting, we look for an optimal equilibrium, which generates larger values than any other equilibrium does on the entire state space. When the discount function is log sub-additive and the state process is one-dimensional, an opt…
Study on knot unknotting numbers and their behavior under connected sums.
problem Behavior of knot unknotting numbers under connected sums.
method Analyzing the band-unknotting number and its sub-additivity properties.
result Infinitely many examples showing unb(K1#K2)<unb(K1)+unb(K2) and unb(K1#K2)<unb(Ki) for i=1,2. A new metric learning scheme for structured data combining graph and feature-space information.
problem Learning a metric from structured data while respecting metric constraints.
method Training metric-constrained linear combinations of dissimilarity matrices, applying graph-based optimization under constraints.
result Our approach can reduce computational complexity by one order of magnitude for some cases.
We show that the Brill-Lindquist initial data provides a counterexample to a Riemannian Penrose inequality with charge conjectured by G. Gibbons. The observation illustrates a sub-additive characteristic of the area radii for the individual connected components of an outermost horizon as a lower bound of the ADM mass.
We show that the asymptotic dimension of box spaces behaves (sub)additively with respect to extensions of groups. As a result, we obtain that for an elementary amenable group, the asymptotic dimension of any of its box spaces is bounded above by its Hirsch length. This bound is shown to be an equality for a large subcl…
This paper studies the question of whether minimal genus Heegaard splittings of exterior spaces of knots which are connected sums are weakly reducible or not. Furthermore it is shown that the Heegaard splittings of the knots used by Morimoto to show that tunnel number can be sub-additive are all strongly irreducible. T…
Paper uses Mirror Descent for efficient risk budgeting portfolios.
problem Computing optimal risk budgeting weights for various risk measures.
method Employed Mirror Descent algorithms in deterministic and stochastic settings.
result Established convergence and quantitative rate for averaged Mirror Descent algorithm.
Study on equivariant Heegaard genus of reducible 3-manifolds with group actions.
problem Understanding the equivariant Heegaard genus of reducible 3-manifolds with group actions.
method Thin position theory for 3-dimensional orbifolds to establish bounds on equivariant Heegaard genus.
result Sharp bounds on equivariant Heegaard genus of reducible manifolds, similar to tunnel number results.
Unified theory of θ-expectations derived from chaotic dynamics.
problem Non-convex stochastic control problems outside G-expectations.
method Spectral theory of transfer operators for uniformly hyperbolic flows, viscosity solutions to HJB equations.
result Affine Hessian, non-convex gradient structure of θ-expectation. To find a trade-off between profitability and prudence, financial practitioners need to choose appropriate risk measures. Two key points are: Firstly, investors' risk attitudes under uncertainty conditions should be an important reference for risk measures. Secondly, risk attitudes are not absolute. For different marke…
A multi-crossing (or n-crossing) is a singular point in a projection at which n strands cross so that each strand bisects the crossing. We generalize the classic result of Kauffman, Murasugi, and Thistlethwaite, which gives the upper bound on the span of the bracket polynomial of K as 4c_2(K), to the n-crossing number:…
Expected Shortfall (ES) in several variants has been proposed as remedy for the defi-ciencies of Value-at-Risk (VaR) which in general is not a coherent risk measure. In fact, most definitions of ES lead to the same results when applied to continuous loss distributions. Differences may appear when the underlying loss di…
This paper identifies and analyzes biases in risk-adjusted index weighting methods, affecting social welfare and market fairness.
problem Biases in risk-adjusted index weighting methods lead to tracking errors and fraud in indices and ETFs.
method Characterizes and analyzes the biases and adverse effects of risk-adjusted index weighting methods.
result These biases reduce social welfare and can enable harmful arbitrage activities.
We consider the problem of risk diversification of α-stable heavy tailed risks. We study the behaviour of the aggregated Value-at-Risk, with particular reference to the impact of different tail dependence structures on the limits to diversification. We confirm the large evidence of sub-additivity violations, particul…
We introduce a new notion of conditional nonlinear expectation under probability distortion. Such a distorted nonlinear expectation is not sub-additive in general, so it is beyond the scope of Peng's framework of nonlinear expectations. A more fundamental problem when extending the distorted expectation to a dynamic se…
Investigates VaR behavior for sums of one-sided random variables, showing impossibilities and conditions for super-additivity.
problem Investigates the behavior of Value-at-Risk (VaR) for sums of one-sided random variables.
method Analyzes the extremal aggregation behavior of VaR, introduces structural conditions for super-additivity.
result Characterizes when VaR is fully super-additive and provides unified framework for various dependence structures.
We present a general framework for measuring the liquidity risk. The theoretical framework defines a class of risk measures that incorporate the liquidity risk into the standard risk measures. We consider a one-period risk measurement model. The liquidity risk is defined as the risk that a given security or a portfolio…
Novel framework for teaching complexity in machine teaching models.
problem Understanding and comparing teaching models in batch and sequential settings.
method Developed a novel framework using preference functions to capture teaching complexity.
result Identified preference functions leading to linear teaching complexity in sequential models.
Paper proves integrability and entropy compactness for Kähler potentials with uniform log-log threshold.
problem Integrability and entropy compactness for Kähler potentials with specific density.
method Skoda-Zeriahi type integrability theorem and log-log threshold detection.
result Positivity of integrability threshold and entropy compactness for uniform log-log threshold.
In this paper, we prove that the zero-locus of any global holomorphic log-one-form on a projective log-smooth pair (X,D) of log-general type must be non-empty. Applying this result, we give an answer to the algebraic hyperbolicity part of Shafarevich's conjecture, with the generic fiber being Kawamata-log-…
We consider active learning with logged data, where labeled examples are drawn conditioned on a predetermined logging policy, and the goal is to learn a classifier on the entire population, not just conditioned on the logging policy. Prior work addresses this problem either when only logged data is available, or purely…
Establishes log-concavity estimates for convex domains' first Dirichlet eigenfunctions.
problem Quantifying the Hessian of log-concave eigenfunctions on convex domains.
method Analyzes log-concavity properties of the first Dirichlet eigenfunction on convex domains.
result Obtains quantitative estimates for the Hessian of logu. Alternative proof of semipositivity and nefness for K-semistable log-Fano pairs.
problem Semipositivity and nefness of Chow-Mumford line bundle for K-semistable log-Fano pairs.
method Alternative proof using families of K-semistable log-Fano pairs.
result Proof of semipositivity and nefness for K-semistable log-Fano pairs.
Study confirms boundedness of certain singularities in log Fano geometry.
problem Boundedness of log Fano cone singularities and minimal log discrepancies.
method Analyzing local volumes and minimal log discrepancies of Kollár components.
result Boundedness of K-semistable log Fano cone singularities confirmed in dimension three.
Study improves sampling from non-log-concave distributions using Fisher information.
problem Sampling from non-log-concave distributions with high Fisher information guarantees.
method Proximal sampler with RGO implementation, leveraging log-concave sampling results.
result Improved complexity guarantee in relative Fisher information for non-log-concave sampling.
New algorithms improve convergence rates for non-log-concave sampling and log-partition estimation.
problem Efficiently sampling from non-log-concave distributions and estimating their log-partition function.
method Analysis of information-based complexity, study of polynomial-time sampling algorithms.
result Optimal rates for sampling and log-partition estimation sometimes exceed those for optimization.
LogAnMeta detects anomalies from log events using meta learning.
problem Poor performance of current log anomaly detection on new or unseen anomalies.
method Meta-learning-based hybrid few-shot classifier trained in an episodic manner.
result Demonstrates efficacy of LogAnMeta on detecting anomalies with few samples.
Defines log Floer cohomology for symplectic surfaces with a degenerate part.
problem Extending Floer cohomology to degenerate symplectic structures.
method Definition of log Floer cohomology for oriented log symplectic surfaces.
result Log Floer cohomology is invariant under isotopies and isomorphic to log de Rham cohomology for a single Lagrangian.
Using stable log maps, we introduce log twisted differentials extending the notion of abelian differentials to the Deligne-Mumford boundary of stable curves. The moduli stack of log twisted differentials provides a compactification of the strata of abelian differentials. The open strata can have up to three connected c…
Test log-likelihood comparisons can be misleading.
problem Misinterpretation of test log-likelihood in model comparison.
method Simple examples of model comparison and forecast accuracy.
result Test log-likelihood does not always correlate with model accuracy.
Constructs Kahler-Einstein metrics near isolated log canonical singularities.
problem Constructing metrics near singularities in complex geometry.
method Constructs Kahler-Einstein metrics with negative scalar curvature near isolated log canonical singularities.
result Metrics are complete near the singularity if the underlying space has complex dimension 2 or if the singularity is smoothable.
We study topological properties of log-symplectic structures and produce examples of compact manifolds with such structures. Notably we show that several symplectic manifolds do not admit log-symplectic structures and several log-symplectic manifolds do not admit symplectic structures, for example #m CP^2 # n bar(CP^2)…
We consider the problem of learning a general graph G=(V,E) using edge-detecting queries, where the number of vertices ∣V∣=n is given to the learner. The information theoretic lower bound gives mlogn for the number of queries, where m=∣E∣ is the number of edges. In case the number of edges m is also given t…
Proves log-concavity of cluster algebra coefficients for type An.
problem Log-concavity of cluster algebra coefficients.
method Introduced atomic theta basis and proved log-concavity for type An. result Proved log-concavity of coefficients for cluster algebra variables of type An. Corrects pseudo log-likelihood method issues in various applications.
problem Log-likelihood function unbounded issues in pseudo log-likelihood methods.
method Provided a counterexample and corrected algorithms in previous literature.
result Ensured well-definedness of maximum pseudo log-likelihood estimation.
In this article we construct a canonical Kähler-Einstein current on a LC (log canonical) pairs of log general type as the limit of a sequence of canonical Kähler-Einstein currents on KLT(Kawamata log terminal) pairs of log general type. We call the volume form associated with the canonical Kähler-Einstein current the c…
The purpose of this article is to develop techniques for estimating basis log canonical thresholds on logarithmic surfaces. To that end, we develop new local intersection estimates that imply log canonicity. Our main motivation and application is to show the existence of Kahler-Einstein edge metrics on all but finitely…
New lower bounds for sampling from log-concave distributions in higher dimensions.
problem Proving lower bounds for sampling from log-concave distributions in higher dimensions.
method Multiscale construction inspired by geometric measure theory and reduction to block Krylov algorithms.
result Query lower bounds for sampling from log-concave distributions in higher dimensions are established.
We leverage a streaming architecture based on ELK, Spark and Hadoop in order to collect, store, and analyse database connection logs in near real-time. The proposed system investigates outliers using unsupervised learning; widely adopted clustering and classification algorithms for log data, highlighting the subtle var…
Dividing deep learning models for consistent anomaly detection in changing log data.
problem Anomaly detection methods fail when log data types change, leading to false negatives.
method Divide deep learning models based on log data correlation and extract correlations.
result Continues anomaly detection accuracy even when log data changes.
Develops log-Euclidean Lie groups for SPD and correlation matrices.
problem Unifies various log-Euclidean constructions for SPD and correlation matrices.
method Theory and explicit isometries linking different log-Euclidean metrics.
result Explicit log-Euclidean metrics on SPD and correlation matrices.
Log-symplectic structures are Poisson structures that are determined by a symplectic form with logarithmic singularities. We construct moduli spaces of curves with values in a log-symplectic manifold. Among the applications, we classify symplectically ruled log-symplectic 4 manifolds (both orientable and non-orientab…
Proves unique degeneration of log Fano fibration germs.
problem Stable degeneration of log Fano fibration germs.
method Introduced the H-invariant for filtrations over log Fano fibration germs and used a unique quasi-monomial valuation to achieve the degeneration.
result Unique K-polystable special degeneration of log Fano fibration germs.