We prove an off-diagonal expansion for a Toeplitz operator with an indicator function.
problem Asymptotics of Toeplitz operators with indicator function
method Off-diagonal expansion
result We extend two results to the non-compact setting.
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48 results for “indicator function”
Paper develops compact formulations for optimization problems with rank-one convex functions and indicator variables.
problem Optimization problems involving rank-one convex functions with support constraints.
method Perspective reformulation techniques to exploit conic structure and establish convex hull results.
result Systematic perspective formulations for convex hull descriptions of sets with nonlinear separable or non-separable objective functions and combinatorial constraints.
On Morse Index Retrievalmath.DG
Proves functions can have two indices differing by two.
problem Understanding Morse index for smooth functions.
method Analyzes functions in unit sphere and ball.
result Exists functions with two indices differing by two.
Paper introduces efficient methods for estimating cross-partial derivatives and sensitivity indices.
problem Efficiently estimating cross-partial derivatives and sensitivity indices in complex models.
method Using randomized points and constraints, the paper develops estimators with optimal convergence rates and low bias.
result The estimators achieve optimal rates of convergence and do not suffer from the curse of dimensionality.
New indices for determining cluster compactness and separability.
problem Challenges in identifying true clusters in data sets.
method Developed absolute cluster indices to measure compactness and separability.
result Demonstrated improved performance compared to existing indices.
Scaling Properites of Price Changes for Korean Stock Indicescond-mat.stat-mech
We consider returns of two Korean stock market indices, KOSPI and KOSDAQ index. Central parts of the probability distribution function of returns are well fitted by the Lorentzian distribution function. However, tail parts of the probability distribution function follow a power law behavior well. We found that the prob…
Strict concavity proven for growth indicator function of certain groups.
problem Proving strict concavity of growth indicator function for specific groups.
method Smoothness of Manhattan hypersurface and critical-exponent map.
result Strict concavity of growth indicator function for relatively Anosov groups.
New estimator for survival function with missing not at random censoring indicators.
problem Estimating survival function with missing not at random censoring indicators.
method Proposes a new estimator based on a conditional copula model for the missingness mechanism.
result Provides a new method for estimating conditional survival function with MNAR censoring indicators.
New algorithm forecasts health indicators for better equipment lifespan prediction.
problem Improving equipment lifespan prediction through health indicator forecasting.
method Generative + scenario matching approach using Gaussian Process.
result Superior performance compared to existing methods.
Prove integrality of genus- indices with adjoint Reidemeister torsions for twist knots and meridians.
problem Prove integrality of genus- indices with adjoint Reidemeister torsions for twist knots and meridians.
method Consider the sum of the adjoint Reidemeister torsions and prove integrality for twist knots and meridians.
result Prove integrality of genus- indices with adjoint Reidemeister torsions for twist knots and meridians.
Improving Estimation of the Koopman Operator with Kolmogorov-Smirnov Indicator Functionsphysics.data-an
The paper proposes a method to improve Koopman operator estimation using indicator functions.
problem Difficulty in identifying good observables for Koopman operator expansion.
method Clustering procedure based on Hidden Markov Model (HMM) to infer surrogate observables.
result Inferred indicator functions significantly improve estimation of Koopman operator eigenvalues and transition timescales.
We provide several new depth-based separation results for feed-forward neural networks, proving that various types of simple and natural functions can be better approximated using deeper networks than shallower ones, even if the shallower networks are much larger. This includes indicators of balls and ellipses; non-lin…
A non-parametric method for ranking stock indices according to their mutual causal influences is presented. Under the assumption that indices reflect the underlying economy of a country, such a ranking indicates which countries exert the most economic influence in an examined subset of the global economy. The proposed …
Study dynamic risk measures and performance indices using distortion functions.
problem Investigate time consistency of dynamic risk measures and performance indices generated by distortion functions.
method Analyze dynamic coherent risk measures (DCRMs) and dynamic weighted value at risk measures, proving their equivalence. Establish properties of families of DCRMs generated by distortion functions and define corresponding dynamic coherent acceptability indices (DCAIs). Examine time consistency of DCRMs and DCAIs.
result DCRM generated by distortion functions are sub-martingale time consistent but not super-martingale time consistent and not weakly acceptance time consistent.
Study uses Hawkes processes to analyze stock market contagion in China.
problem Understanding contagion in Chinese stock market.
method Fitting Hawkes processes to daily returns and sector indices.
result Identifies long-term dependencies and trending patterns in sector indices.
The paper evaluates integrals for fBm with various Hurst indices.
problem Evaluating integrals for stochastic processes with fractional Brownian motion for different Hurst indices.
method Analytic continuation from complex analysis to extend integral domain.
result Integral formulas for fBm with Hurst indices are derived.
This paper simplifies conditional Sobol' indices calculation using PCE bases.
problem Computational inefficiency and lack of consistency in evaluating conditional Sobol' indices.
method Analytical extraction of conditional Sobol' indices via basis decomposition of PCE expansions.
result Derives closed-form expressions for conditional Sobol' indices.
We describe the configuration space of polygons with prescribed edge slopes, and study the perimeter as a Morse function on . We characterize critical points of (these are \textit{tangential} polygons) and compute their Morse indices. This setup is motivated by a num…
The counting function on the natural numbers defines a discrete Morse-Smale complex with a cohomology for which topological quantities like Morse indices, Betti numbers or counting functions for critical points of Morse index are explicitly given in number theoretical terms. The Euler characteristic of the Morse filtra…
New spectral invariants distinguish Joyce orbifolds from other manifolds.
problem Distinguishing Joyce orbifolds from other -structures.
method Introducing and computing two new spectral invariants for Joyce orbifolds.
result These invariants are more effective than existing invariants for distinguishing Joyce orbifolds.
Kjolstad et. al. proposed a tensor algebra compiler. It takes expressions that define a tensor element-wise, such as , and generates the corresponding compute kernel code. For machine learning, especially deep learni…
Investigates the relationship between US money supply and asset indices over 2001-2019.
problem Determining the relationship between US money supply and asset indices growth.
method Information entropy methodology applied to US asset indices (Property, Russell 2000, S&P 500, NASDAQ) over 2001-2019.
result Growth in US broad money supply is the main determinant of US asset indices growth, especially the NASDAQ and Russell 2000.
Develops virtual Morse-Bott indices for four-manifolds, proving inequalities.
problem Proving inequalities for four-manifolds of Seiberg-Witten simple type.
method Uses virtual Morse-Bott indices and Hirzebruch-Riemann-Roch Theorem.
result Proves positivity of virtual Morse-Bott indices, leading to inequalities.
Federated learning calibrates insurance indices from renewable energy producers' data.
problem Calibrating parametric insurance indices under heterogeneous renewable energy production losses.
method Federated learning framework using Tweedie GLMs and distributed optimization.
result Federated learning recovers comparable index coefficients under moderate heterogeneity.
This work formalizes and extends parameter sharing in multi-agent reinforcement learning.
problem Parameter sharing limits multi-agent learning to a single policy, preventing different tasks or action spaces.
method Introduces agent indication and extends parameter sharing to heterogeneous observation and action spaces.
result Proves convergence to optimal policies for parameter sharing in heterogeneous environments.
The paper bounds growth indicator functions for discrete subgroups in algebraic groups.
problem Bounding growth indicator functions for discrete subgroups in algebraic groups.
method Pointwise bound and equality conditions for growth indicator functions.
result Strict inequalities and equality conditions for growth indicator functions.
An explicit martingale representation for random variables described as a functional of a Levy process will be given. The Clark-Ocone theorem shows that integrands appeared in a martingale representation are given by conditional expectations of Malliavin derivatives. Our goal is to extend it to random variables which a…
This work presents deep asymmetric networks with a set of node-wise variant activation functions. The nodes' sensitivities are affected by activation function selections such that the nodes with smaller indices become increasingly more sensitive. As a result, features learned by the nodes are sorted by the node indices…
Comparison of volatility distributions in the periods of booms and stagnations: an empirical study on stock price indicesphysics.soc-ph
The aim of this paper is to compare statistical properties of stock price indices in periods of booms with those in periods of stagnations. We use the daily data of the four stock price indices in the major stock markets in the world: (i) the Nikkei 225 index (Nikkei 225) from January 4, 1975 to August 18, 2004, of (ii…
Study on phase transitions on surfaces using Allen-Cahn equation.
problem Existence of critical points with specific nodal sets on surfaces.
method Analysis of Allen-Cahn functional on compact surfaces, focusing on nodal sets and energy.
result Existence of countable families of critical points with nodal sets converging to geodesics.
Based on Colombeau's theory of algebras of generalized functions we introduce the concepts of generalized functions taking values in differentiable manifolds as well as of generalized vector bundle homomorphisms. We study their basic properties, in particular with respect to some new point value concepts for generalize…
Study examines cryptocurrency impacts on financial indices using advanced risk models.
problem Interdependence between cryptocurrencies and financial indices, focusing on risk spillover.
method Hybrid approach integrating GARCH, EVT, and copula functions for risk measures.
result eGARCH-EVT-Copula model outperforms conventional methods in risk estimation.
Even before deep learning architectures became the de facto models for complex computer vision tasks, the softmax function was, given its elegant properties, already used to analyze the predictions of feedforward neural networks. Nowadays, the output of the softmax function is also commonly used to assess the strength …
Time-varying neural network improves stock return prediction.
problem Predicting stock returns in a time-varying market.
method Online early stopping algorithm for neural network training.
result The proposed algorithm outperforms current methods in predicting monthly U.S. stock returns.
Non-negative -approximating polynomials for Gaussian distributions are proven for certain classes of sets.
problem Existence of non-negative -approximating polynomials for Gaussian distributions.
method Proving the existence of degree- non-negative polynomials that approximate indicator functions of sets with Gaussian surface area in -norm.
result Proves the existence of non-negative -approximating polynomials for certain classes of sets with Gaussian surface area.
After having given the general variational formula for the functionals indicated in the title, the critical points of the integral of the equi-affine curvature under area constraint and the critical points of the full-affine arc-length are studied in greater detail.
Paper proposes a cost-sensitive conformal training method with provably controllable learning bounds.
problem Uncertainty quantification and learning bounds in conformal prediction.
method Cost-sensitive conformal training algorithm that minimizes the expected size of prediction sets using rank weighting.
result Theoretical analysis shows tightness between weighted objective and expected size of conformal prediction sets.
A discrete system's heterogeneity is measured by the Rényi heterogeneity family of indices (also known as Hill numbers or Hannah--Kay indices), whose units are {the numbers equivalent}. Unfortunately, numbers equivalent heterogeneity measures for non-categorical data require {a priori} (A) categorical partitioning and …
BOtied optimizes multiple objectives using copulas and CDF indicators.
problem Joint optimization of multiple competing objectives.
method Proposes BOtied, a new acquisition function based on the CDF.
result BOtied outperforms state-of-the-art MOBO acquisition functions.
Proposes a method to partition univariate data into unimodal subsets.
problem Partitioning univariate multimodal data into unimodal subsets.
method Recursive splitting around valley points of the data density using properties of critical points on the convex hull of the ecdf plot.
result Obtains a hierarchical statistical model of the initial dataset as a mixture of UMMs.
In this paper, we present a method for the accurate estimation of the derivative (aka.~sensitivity) of expectations of functions involving an indicator function by combining a stochastic algorithmic differentiation and a regression. The method is an improvement of the approach presented in [Risk Magazine April 2018]. T…
Distance function to a finite set is a topological Morse function.
problem Characterizing the topological Morse function of a finite set.
method Analyzing the distance function to a finite set in \(\mathbb{R}^n\).
result Distance function is a topological Morse function, with precise critical points and indices.
Indices of acceptability are well suited to frame the axiomatic features of many performance measures, associated to terminal random cash flows.We extend this notion to classes of càdlàg processes modelling cash flows over a fixed investment horizon.We provide a representation result for bounded paths. We suggest an ac…
A method for interpreting SVMs using polynomial kernels, revealing model complexity.
problem Interpreting SVMs built with truncated orthogonal polynomial kernels.
method Orthogonal Representation Contribution Analysis (ORCA) with normalized Orthogonal Kernel Contribution (OKC) indices.
result The method reveals structural aspects of model complexity not captured by predictive accuracy.
This paper introduces and develops a novel variable importance score function in the context of ensemble learning and demonstrates its appeal both theoretically and empirically. Our proposed score function is simple and more straightforward than its counterpart proposed in the context of random forest, and by avoiding …
We study the effect of the social stratification on the wealth distribution on a system of interacting economic agents that are constrained to interact only within their own economic class. The economical mobility of the agents is related to its success in exchange transactions. Different wealth distributions are obtai…
Markov random fields (MRFs) are difficult to evaluate as generative models because computing the test log-probabilities requires the intractable partition function. Annealed importance sampling (AIS) is widely used to estimate MRF partition functions, and often yields quite accurate results. However, AIS is prone to ov…
How not to Stitch Representations to Measure Similarity: Task Loss Matching versus Direct Matchingcs.LG
Task loss matching misrepresents similarity between neural network layers.
problem Measuring similarity between neural network layers using task loss matching.
method Task loss matching vs. direct matching; comparison with CCA and CKA.
result Direct matching provides a better similarity index than task loss matching.