Study shows certain spin manifolds can't meet DEC condition.
problem Non-existence of spin fill-ins meeting DEC condition.
method Analyzes spin Riemannian manifolds and generalized mean curvature functions.
result Closed spin manifolds cannot satisfy DEC if curvature is large.
Smooth dec initial data sets may not extend to smooth spacetimes.
problem Whether every dec initial data set can be extended to a smooth spacetime.
method Examined the converse of the dominant energy condition for initial data sets and spacelike hypersurfaces.
result Not all dec initial data sets can be extended to smooth spacetimes.
Expectation maximization (EM) has recently been shown to be an efficient algorithm for learning finite-state controllers (FSCs) in large decentralized POMDPs (Dec-POMDPs). However, current methods use fixed-size FSCs and often converge to maxima that are far from optimal. This paper considers a variable-size FSC to rep…
Local DEC formulation handles anisotropic materials efficiently.
problem Efficiently modeling material anisotropy in 2D simulations.
method Local formulation of 2D Discrete Exterior Calculus (DEC) for anisotropic materials.
result Robust DEC discretization of anisotropic fluxes and 1-forms.
Geometric DEC solves Poisson on general triangulations.
problem Solving Poisson equation on arbitrary triangulations.
method Revisited Discrete Exterior Calculus (DEC) for general triangulations using Vector Calculus and Matrix Algebra.
result DEC solutions match FEML for Poisson equation.
New bounds for γ-regret using modified Decision-Estimation Coefficient.
problem Statistical characterization of γ-regret for complex bandit problems. method Statistical characterization via γ-DEC, a modified Decision-Estimation Coefficient. result Upper and lower bounds for γ-regret nearly match, showing fundamental limits. We solve surface Navier-Stokes using DEC and compare with vorticity-stream function.
problem Solving the surface Navier-Stokes equation numerically.
method Discrete exterior calculus (DEC) in space and semi-implicit time discretization.
result Second order convergence demonstrated in flat space discretization.
DECS tool assesses swap rates of DEXes and Fusion outperforms competitors.
problem Lack of unbiased swap rate comparisons in decentralized finance.
method Swap transaction monitoring and simulation techniques.
result 1inch Classic and Fusion consistently outperform competitors in swap rates.
Discrete exterior calculus shows natural properties of wedge product and averaging.
problem Naturalness of discrete exterior calculus operations.
method Showed naturalness of discrete wedge product and averaging interpretation.
result Discrete wedge product is natural and equals Wilson's cochain product.
Unified algorithm tackles various RL goals like reward-free and preference-based learning.
problem Unified approach to multiple RL learning goals.
method Decision-Estimation Coefficient (DEC) framework.
result Unified algorithm handles various learning goals with a single framework.
Operational guide to discrete exterior calculus on cubic cells.
problem Applying calculus on discrete manifolds.
method Defining discrete exterior calculus on cubic cells for discrete manifolds.
result Gauss and Stokes theorems are recovered on the discrete torus.
New DEC variant improves sample complexity bounds in decision making.
problem Understanding sample-efficient learning guarantees in decision making.
method Introducing a new Constrained Decision-Estimation Coefficient (DEC) and using it to derive improved lower bounds.
result New lower bounds improve upon prior work in three aspects: expectation, global applicability, and improper reference models.
For a principal bundle P→M equipped with a connection Aˉ, we study an infinite dimensional bundle PAˉdecP over the space of paths on M, with the points of PAˉdecP being horizontal paths on P decorated with elements of a second structure group. We co…
A decentralized algorithm for high-dimensional Bayesian optimization.
problem Scalability and interdependent effects in high-dimensional optimization.
method Sparse factor graph representation for efficient decentralized optimization.
result Guaranteed no-regret performance in decentralized optimization.
We derive a numerical method for Darcy flow, hence also for Poisson's equation in mixed (first order) form, based on discrete exterior calculus (DEC). Exterior calculus is a generalization of vector calculus to smooth manifolds and DEC is one of its discretizations on simplicial complexes such as triangle and tetrahedr…
Parallelizes DEC on curved meshes using group actions.
problem Efficiently solving DEC operators on curved and 3D meshes.
method Universal block-diagonalization framework for d and ⋆ operators, exploiting group actions. result Block-diagonal structure inherited by operators, enabling parallel solvers.
Improves decision complexity in hybrid environments.
problem Complexity in hybrid decision-making problems.
method General extension of DEC framework, model aggregation approach.
result Improved regret bounds for linear Q*/V* MDPs.
Deep learning models predict stock prices with high accuracy and speed.
problem Precise prediction of stock prices in an efficient market.
method Design and training of ten deep learning regression models.
result Models achieve high accuracy in forecasting stock prices of an auto sector company.
We propose a mathematical procedure for finding informed traders in ultra-high frequency trading. We wrote it as Vector ARMA and found condition of its stationarity. For the price exposure complied with ARMA(1,2) we proved that underlying asset price difference can be derived as ARMA(1,1) process. For validation of the…
Study distance and intersection number in curve graphs of surfaces.
problem Understanding the relationship between distance and intersection number in curve graphs of surfaces.
method Introduced efficient geodesics and studied rectangles called spirals in the cellular decomposition.
result Developed an algorithm to reduce intersection number while preserving distance.
The paper proves positive mass theorems for initial data sets with noncompact boundaries.
problem Proving positive mass theorems for initial data sets with noncompact boundaries.
method Defining an energy-momentum vector at spatial infinity and proving positive mass inequalities under DECs.
result Proves positive mass inequalities for initial data sets with noncompact boundaries under suitable DECs.
Framework for robust decision making in changing environments with privacy constraints.
problem Interactive decision making in changing environments with constraints.
method Hybrid Decision Making with Structured Observations (hybrid DMSO) framework, local differentially private decision making, query-based learning, robust and smooth decision making.
result Strong connections and bounds derived for DEC, SQ dimension, local minimax complexity, learnability, and joint differential privacy.
A conservative discretization of incompressible Navier-Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equatio…
In this article we investigate the restrictions imposed by the dominant energy condition (DEC) on the topology and conformal type of \textsl{possibly non-compact} marginally outer-trapped surfaces (thus extending Hawking's classical theorem on the topology of black holes). We first prove that an unbounded, stable margi…
Proves properties of free boundary stable MOTS in spacetimes.
problem Topology of black hole spacetimes in manifolds with boundary.
method Initial data version of Hawking's theorem, foliation by MOTS, vanishing null second fundamental form.
result Compact free boundary stable MOTS in initial data sets with boundary are of positive Yamabe type.
Paper discusses quasilocal mass and fill-ins, proving positivity and exploring definitions.
problem Exploring and defining quasilocal mass and fill-ins in general relativity.
method Analyzes several proposals of quasilocal mass based on Hamiltonian formulation and proves positivity under certain conditions.
result Positivity of Wang-Yau energy under a more general condition.
CV outperforms mean-variance for stock returns, minimizing risk and maximizing growth.
problem Traditional risk assessment methods underperform in stock market analysis.
method Derived new CV equation and used it to analyze stock performance.
result Stocks with low but positive CV grow exponentially, outperforming high-risk stocks.
This study evaluates different portfolio designs for Indian stocks.
problem Optimizing portfolio weights for risk and return in volatile stock markets.
method Three portfolio design approaches: risk minimization, risk optimization, and equal weighting. Historical data from 2017-2022 used.
result Equal-weight portfolios outperformed other designs in most sectors.
The probability distribution of stock price changes is studied by analyzing a database (the Trades and Quotes Database) documenting every trade for all stocks in three major US stock markets, for the two year period Jan 1994 -- Dec 1995. A sample of 40 million data points is extracted, which is substantially larger tha…
The study predicts stock volatility using LSTM and GARCH models.
problem Accurately predicting stock price volatility is challenging.
method Multiple volatility models (GARCH, GJR-GARCH, EGARCH, LSTM) applied to three sectors.
result LSTM outperformed other models in pharma sector volatility prediction.
This study optimizes stock portfolios for Indian sectors using historical data.
problem Challenges in optimizing stock portfolios due to volatility and future value estimation.
method Used Sharpe, Sortino, and Calmar ratios to design mean-variance optimized portfolios.
result Identified the ratio that maximizes cumulative returns for most sectors.
Unified framework for lower bounds in interactive decision making.
problem Challenges in interactive decision making, especially bandits and reinforcement learning.
method Interactive Fano method and Fractional Covering Number.
result Unified characterization of learnability for stochastic bandit problems and tight lower bounds for interactive decision making.
The correlation function of a financial index of the New York stock exchange, the S&P 500, is analyzed at 1 min intervals over the 13-year period, Jan 84 -- Dec 96. We quantify the correlations of the absolute values of the index increment. We find that these correlations can be described by two different power laws wi…
StoryGen uses images to generate coherent text from multiple images.
problem Generating coherent text from multiple images.
method Designing a Relational Text Data Generator algorithm to relate features from plural images.
result The model can generate meaningful paragraphs containing extracted features from input images.
We propose a mathematical model for the word-of-mouth communications among stock investors through social networks and explore how the changes of the investors' social networks influence the stock price dynamics and vice versa. An investor is modeled as a Gaussian fuzzy set (a fuzzy opinion) with the center and standar…
New algorithms reduce sample complexity for multiclass contextual bandits.
problem Designing efficient algorithms for multiclass contextual bandits with sparse rewards.
method Two complementary approaches: decision-estimation coefficient analysis and low-variance exploration.
result Achieved optimal sample complexity bounds for multiclass contextual bandits.
We study the statistical properties of volatility---a measure of how much the market is likely to fluctuate. We estimate the volatility by the local average of the absolute price changes. We analyze (a) the S&P 500 stock index for the 13-year period Jan 1984 to Dec 1996 and (b) the market capitalizations of the largest…
A new comprehensive approach to nonlinear time series analysis and modeling is developed in the present paper. We introduce novel data-specific mid-distribution based Legendre Polynomial (LP) like nonlinear transformations of the original time series Y(t) that enables us to adapt all the existing stationary linear Gaus…
Study shows demonetization strengthened Indian currency and stock market.
problem Impact of demonetization on Indian stock market and foreign exchange rate.
method Daily rate of return analysis of foreign exchange rate and Nifty 50 index, use of dummy variable for demonetization period.
result Demonetization led to an upward trend in Indian stock market and strengthened the Indian currency (decreased foreign exchange rate).
Model predicts and optimizes trading of electricity price spreads across multiple zones.
problem Forecasting and optimizing day-ahead versus real-time price spreads in U.S. electricity markets.
method Unified statistical model for positive and negative spikes, structural price impact model based on bid stacks.
result Optimal trading strategy improves risk-return profile and highlights market heterogeneity.
This paper optimizes portfolios using HRP and CLA algorithms on NIFTY 50 stocks.
problem Designing an optimal stock portfolio with accurate forecasting of future returns and risks.
method Uses hierarchical risk parity and critical line algorithms on NIFTY 50 stocks.
result Hierarchical risk parity algorithm outperformed the critical line algorithm on test data.
The paper uses LSTM to predict stock prices and optimize portfolio weights.
problem Accurate prediction of stock prices and designing optimized portfolios.
method Built sector-wise portfolios and an LSTM model for stock price prediction.
result The LSTM model accurately predicts stock prices with high accuracy.
This paper optimizes portfolios of thematic sector stocks using LSTM models.
problem Designing an optimized portfolio of stocks to maximize return and minimize risk.
method Extracted stock prices from Jan 2016 to Dec 2020, used LSTM model for prediction, designed portfolios based on critical stocks.
result LSTM model accurately predicted future stock returns, indicating high accuracy.
This study compares two portfolio optimization methods on Indian stocks.
problem Designing an optimal portfolio considering stock returns and risks.
method Hierarchical Risk Parity and Eigen Portfolio approaches on NIFTY 50 sectors.
result Hierarchical Risk Parity portfolio outperforms Eigen portfolio in most sectors tested.
Framework reduces contextual bandit learning to offline regression with near-optimal regret.
problem Efficient learning with large action spaces and complex reward functions.
method Offline Estimation to Decisions (OE2D) algorithm that minimizes regret with near-optimal oracle calls.
result Near-optimal regret for contextual bandits with large action spaces and O(log(T)) offline oracle calls. OE2D framework reduces contextual bandits to offline regression for near-optimal regret.
problem Efficiently learning contextual bandits with large action spaces and complex reward functions.
method Offline Estimation to Decisions (OE2D) algorithm that reduces contextual bandits to offline regression.
result Near-optimal regret for contextual bandits with large action spaces and O(logT) calls to an offline regression oracle. This paper uses cointegration to identify profitable pair-trading strategies for Indian stocks.
problem Finding profitable pair-trading opportunities in Indian stock market.
method Cointegration analysis to identify co-movement stocks, forming pairs, evaluating portfolios.
result Pairs from auto and realty sectors generally yielded the highest returns, while IT sector pairs had negative returns.
BIG Laplacians bridge combinatorial and Hodge Laplacians for discrete data.
problem Comparing combinatorial and Hodge Laplacians for discrete data.
method Introducing Boundary-Induced Graph (BIG) Laplacians using DEC.
result BIG Laplacian eigenvalues converge to Hodge Laplacian for simple shapes.