A Power Transformcs.LG
Novel power transform unifies various mathematical functions.
problem Normalizing and standardizing datasets.
method Presented a novel power transform.
result Unified various mathematical functions.
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48 results for “power function”
Paper examines power consumption in neural networks using various activation functions.
problem Power consumption in machine learning models.
method Examines power consumption for different activation functions.
result Substantial differences in power consumption exist between activation functions.
The paper establishes conditions for strict power concavity in convolutions.
problem Conditions for strict power concavity in convolutions.
method Analyzes sufficient conditions for strict parabolic power concavity of convolutions.
result Establishes sufficient conditions for strict power concavity of convolutions.
The paper calculates asymptotic expansions for specific types of oscillatory integrals.
problem Analyzing oscillatory integrals with complex phase functions.
method Using asymptotic expansions of simpler phase functions to derive results for more complex cases.
result Explicit computation of coefficients in asymptotic expansions for certain integrals.
Sharp lower bound on GHHs' representation power of CPWL functions.
problem Proving the minimum number of nestings for GHHs to represent arbitrary CPWL functions.
method Using a key lemma about finite sums of periodic functions, proving necessity of n nestings.
result Proving necessity of n nestings for GHHs to achieve universal representation power.
Study of metrics on positive-definite matrices from power potential, linking to power means.
problem Understanding metrics on positive-definite matrices derived from power potential.
method Explicit expressions for geodesics and distance function derived from Hessian of power potential.
result Geodesics and distance function converge to weighted matrix geometric mean as β tends to zero.
Investigates neural network approximation power with bounds.
problem Understanding neural network capacity for approximation.
method Established lower and upper bounds on network size and difference.
result Improved bounds for certain function classes.
Deep RL optimizes power control for wireless multicast systems.
problem Optimal power control is intractable due to a large state space.
method Deep reinforcement learning with function approximation via neural networks.
result Optimal power control can be learned for large systems.
The paper proves the concavity of -entropy power and applies it to functional inequalities.
problem Proving concavity of -entropy power on Riemannian manifolds.
method Analyzing the -heat equation on closed Riemannian manifolds with nonnegative Ricci curvature.
result New proofs and improvements of -Euclidean Nash and Logarithmic Sobolev inequalities.
Study finds solutions to flows by negative curvature powers.
problem Curvature flows with negative powers.
method Closed self-similar solutions in warped product manifolds, proving non-strict convexity.
result Proves self-similar solutions are slices of warped product manifolds.
An explicit formula for the discrete power function associated with circle patterns of Schramm typenlin.SI
We present an explicit formula for the discrete power function introduced by Bobenko, which is expressed in terms of the hypergeometric τfunctions for the sixth Painlevé equation. The original definition of the discrete power function imposes strict conditions on the domain and the value of the exponent. However, we sh…
We present a formula for the trace of any symmetric power of a matrix (with coefficients in a field) in terms of the ordinary powers of the matrix, an arbitrarily chosen linear function which vanishes on the identity matrix, and polynomial functions defined recursively.
Bayesian method models multivalued power data from wind farms.
problem Accurate modeling of power curves with multivalued relationships.
method Overlapping mixture of probabilistic regression models.
result Model accurately represents practical power data.
Study explores how scalar functionals evolve under Ricci flow.
problem Understanding the evolution of functionals involving scalar quantities under Ricci flow.
method Deriving explicit expressions for the time derivative of integrals of scalar functionals under extended Ricci flow.
result Explicit expressions for the time derivative of integrals involving scalar functionals under Ricci flow.
Unified representation of density-power-based divergences simplifies estimation to M-estimation.
problem Outliers in density estimation.
method Define a norm-based Bregman density power divergence (NB-DPD) that reduces to M-estimation.
result NB-DPD connects and generalizes existing divergences, highlighting robustness properties.
Improved neural network training for speech recognition using power-law nonlinearity and uniform distribution criterion.
problem Stability and uniformity of feature distribution in neural network training.
method Power-function based and histogram-based Maximum Uniformity of Distribution (MUD) algorithms.
result Power-function based MUD outperforms conventional MFCCs in speech recognition systems.
Paper detects and estimates breaks in high-dimensional functional time series.
problem Detecting and estimating structural breaks in heterogeneous mean functions of high-dimensional functional time series.
method Proposes a new test statistic combining functional CUSUM and power enhancement components, with a clustering algorithm for group structure estimation.
result The proposed techniques have satisfactory performance in finite samples, detecting and estimating breaks effectively.
Analytic pairs in 3D space constructed via power series.
problem Constructing analytic pairs of conjugate functions in 3D.
method Exploiting an ansatz to create power series expansions.
result Found entire solutions not harmonic and a 2-parameter family.
For a symplectic manifold with quantizing line bundle, a choice of almost complex structure determines a Laplacian acting on tensor powers of the bundle. For high tensor powers Guillemin-Uribe showed that there is a well-defined cluster of low-lying eigenvalues, whose distribution is described by a spectral density fun…
Regression-based Inverter Control for Decentralized Optimal Power Flow and Voltage Regulationeess.SY
The paper proposes a data-driven method for optimal power flow and voltage regulation in distribution grids.
problem Optimal power flow and voltage regulation in decentralized power grids.
method The approach uses a network model, historic data, and regression to find functions approximating optimal reactive power injections for inverters.
result The method achieves near-optimal results in voltage- and capacity-constrained loss minimization and voltage flattening.
A new family of stochastic dominance orders based on distortion functions.
problem Determining a continuum of dominance relations for risk assessment.
method Introducing H-distorted stochastic dominance, a generalized family of stochastic orders.
result Power-distorted stochastic dominance is particularly appealing due to its simplicity and statistical interpretations.
The paper introduces a new method for estimating optimal policies in dynamic treatment regimes using information geometry.
problem Estimating optimal policies in dynamic treatment regimes.
method Minimum information divergence method based on -power divergence.
result The -power divergence method effectively seeks the optimal policy by vanishing the divergence between policy-equivalent Q-functions.
Deep RL improves power control and scheduling for wireless multicast systems.
problem Scalable power control and scheduling for wireless multicast networks.
method Deep reinforcement learning with function approximation using a deep neural network.
result Deep RL can learn optimal power control policies for large systems.
On the origin of power law tails in price fluctuationscond-mat.stat-mech
In a recent Nature paper, Gabaix et al. \cite{Gabaix03} presented a theory to explain the power law tail of price fluctuations. The main points of their theory are that volume fluctuations, which have a power law tail with exponent roughly -1.5, are modulated by the average market impact function, which describes the r…
A mechanism to derive multi-power law functions: an application in the econophysics frameworkphysics.data-an
It is generally recognized that economical systems, and more in general complex systems, are characterized by power law distributions. Sometime, these distributions show a changing of the slope in the tail so that, more appropriately, they show a multi-power law behavior. We present a method to derive analytically a tw…
The study finds that only round spheres shrink self-similarly under certain curvature flows.
problem Investigating self-similar solutions to curvature flows by high powers of curvature.
method Analyzing closed strictly convex hypersurfaces in under specific curvature flows.
result Only round spheres shrink self-similarly under the studied curvature flows.
Neural Power Unitscs.LG
Neural Power Unit (NPU) learns arbitrary power functions on real numbers.
problem Neural Networks struggle with generalizing beyond seen data and arithmetic operations.
method Introduces Neural Power Unit (NPU) that operates on real numbers and learns arbitrary power functions.
result NPU outperforms competitors in accuracy and sparsity on arithmetic datasets and discovers governing equations from data.
Deep neural networks can approximate complex functions through repeated compositions of a fixed-size ReLU network.
problem Understanding the expressive power of deep neural networks through function compositions.
method Demonstrated the surprising expressive power of repeated compositions of a single fixed-size ReLU network.
result Repeated compositions of a single fixed-size ReLU network can approximate 1-Lipschitz continuous functions on with an error .
The Logarithmic Singularities of the Green Functions of the Conformal Powers of the Laplacianmath.DG
Green functions play an important role in conformal geometry. In this paper, we explain how to compute explicitly the logarithmic singularities of the Green functions of the conformal powers of the Laplacian. These operators include the Yamabe and Paneitz operators, as well as the conformal fractional powers of the Lap…
Study examines multifractality in European power loads over 5 years.
problem Understanding multifractality in European power load time series.
method Applied Multifractal Detrended Fluctuation Analysis (MF-DFA) with improved methodology.
result European power loads exhibit multifractality in both distribution and autocorrelation functions.
Quantized neural networks can represent all fixed-point functions under certain conditions.
problem Expressive power of quantized neural networks under fixed-point arithmetic.
method Analyzing necessary and sufficient conditions for quantized networks to represent all fixed-point functions.
result Various popular activation functions satisfy the sufficient condition for representing all fixed-point functions.
Combines absolute and relative wealth in portfolio optimization with power utility functions.
problem Optimizing portfolios with both absolute and relative wealth considerations.
method Integrates power utility functions for absolute and relative wealth, considering multiple benchmarks.
result Obtains an explicit solution for portfolio optimization combining absolute and relative wealth.
Grouped Gaussian Processes improve solar power and wind speed forecasting.
problem Forecasting distributed solar power and wind speed at multiple sites.
method Coupled Gaussian process priors over groups of node and weight functions.
result Our approach maintains or improves point-prediction accuracy and provides better quantification of predictive uncertainties.
Power Law Distributions in Korean Household Incomescond-mat.stat-mech
We investigate the distribution function and the cumulative probability for Korean household incomes, i.e., the current, labor, and property incomes. For our case, the distribution functions are consistent with a power law. It is also showed that the probability density of income growth rates almost has the form of a e…
Deep actor-critic learning optimizes power control in mobile networks.
problem Optimizing power control in large-scale wireless mobile networks.
method Multi-agent deep reinforcement learning with deep deterministic policy gradient.
result The algorithm maximizes a global utility function in a distributed manner.
Derives spectral density function for symplectic manifolds.
problem Calculating spectral density functions on symplectic manifolds.
method Explicit local formula derivation for spectral density function.
result Explicit formula for spectral density function.
We revisit the optimal investment and consumption problem with proportional transaction costs. We prove that both the value function and the slopes of the lines demarcating the no-trading region are analytic functions of cube root of the transaction cost parameter. Also, we can explicitly calculate the coefficients of …
Market lawsq-fin.ST
Power laws detected in financial data, modeled with random multipliers.
problem Detecting power laws in financial data.
method Investigated data from financial instruments, proposed a model based on sums of Maxwell-Boltzmann distributions with random multipliers.
result Detected power laws with various exponents in financial data, proposed a universal model.
Graph isomorphism can be tested using GNNs, proving their expressive power.
problem Testing graph isomorphism using Graph Neural Networks (GNNs).
method Equivalence between GNNs' function approximation and graph isomorphism testing, using sigma-algebra.
result Equivalence between graph isomorphism testing and GNN function approximation.
Deep polynomial neural networks measure their expressiveness by the dimension of their functional space.
problem Measuring the expressiveness of deep polynomial neural networks.
method Analyzing the algebraic variety defined by the polynomial neural network's weights and activations.
result The dimension of the algebraic variety is a precise measure of the network's expressiveness.
New method explains GNNs using power iteration clustering.
problem Mysterious mechanism of message passing in GNNs.
method Subspace power iteration clustering (SPIC) models.
result Message passing in GNNs can be understood through power iteration.
We study power expansions of the characteristic function of a linear operator in a -dimensional superspace . We show that traces of exterior powers of satisfy universal recurrence relations of period . `Underlying' recurrence relations hold in the Grothendieck ring of representations of $\GL(V)$. The…
Power weighted shortest paths improve clustering of high-dimensional data.
problem Clustering high-dimensional Euclidean data with disjoint low-dimensional manifolds.
method Use of power weighted shortest path distance functions and a fast algorithm.
result Higher clustering accuracy achieved through power weighted shortest paths.
Ubiquitous power law scaling in nonlinear self-excited Hawkes processescond-mat.stat-mech
New mechanism found for power laws including Zipf's law.
problem Understanding the ubiquity of power law distributions.
method Introduced nonlinear self-excited Hawkes processes with fast-accelerating intensities.
result Wide class of nonlinear Hawkes processes have power law intensity PDFs.
DeepGDL models create realistic power grids from confidential data.
problem Creating realistic power grids from confidential data.
method Graph distribution learning (GDL) with a deep nonlinear recurrent structure.
result DeepGDL models accurately create synthetic power grids.
We derive the implied volatility estimation formula in European power call options pricing, where the payoff functions are in the form of and ()respectively. Using quadratic Taylor approximations, We develop the computing formula of implied volatility in European power call op…
New limits found for power, speed, and precision in physical communication.
problem Limits on power, speed, and precision in physical communication.
method Derivation involving a novel connection between friction and information geometry.
result Product of precision and speed is universally bounded by power dissipation.
Study finds financial market data follows power-law exponents typical of stochastic processes.
problem Testing long-range memory in financial markets.
method Analyzed empirical return and trading activity time series from Forex.
result Power-law exponents of burst and inter-burst duration probability density functions are close to 3/2.