Optimal strategy found for minimizing loss in shopper's dilemma.
problem Minimizing loss in a two-period decision-making process.
method Derived from the two-envelope paradox and Black Friday promotion.
result Optimal strategy found to minimize expected loss.
These are notes from the lecture of Devavrat Shah given at the autumn school "Statistical Physics, Optimization, Inference, and Message-Passing Algorithms", that took place in Les Houches, France from Monday September 30th, 2013, till Friday October 11th, 2013. The school was organized by Florent Krzakala from UPMC & E…
Study finds biotech stocks perform better on Wednesdays and Thursdays.
problem Day-of-the-week effect on biotechnology stocks performance.
method Daily returns analysis using GARCH processes and asymmetric GARCH models.
result Biotechnology stocks have higher returns on Wednesdays, Thursdays, and Fridays.
The Nasdaq Composite fell another ≈10 on Friday the 14'th of April 2000 signaling the end of a remarkable speculative high-tech bubble starting in spring 1997. The closing of the Nasdaq Composite at 3321 corresponds to a total loss of over 35% since its all-time high of 5133 on the 10'th of March 2000. Simil…
Study quantifies pedestrian traffic patterns in NYC.
problem Understanding pedestrian traffic dynamics in urban areas.
method Publicly available traffic camera data in NYC, time series analysis.
result Pedestrian traffic exhibits diurnal patterns with weekday peaks and no peak on weekends.
We construct new classes of exact solutions of the 4D vacuum Einstein equations which describe ellipsoidal black holes, black tori and combined black hole -- black tori configurations. The solutions can be static or with anisotropic polarizations and running constants. They are defined by off--diagonal metric ansatz wh…
Using black-hole inequalities and the increase of the horizon's areas, we show that there are arbitrarily small electro-vacuum perturbations of the standard initial data of the extreme Reissner-Nordstrom black-hole that, (by contradiction), cannot decay in time into any extreme Kerr-Newman black-hole. This proves the e…
Mass inequality for black ring spacetimes, showing extreme solutions.
problem Establishing mass-angular momentum relation for black ring spacetimes.
method Mathematical derivation of mass-angular momentum inequality.
result The inequality is saturated for extreme Pomeransky-Sen'kov black ring solutions.
Over the past three decades, black holes have played an important role in quantum gravity, mathematical physics, numerical relativity and gravitational wave phenomenology. However, conceptual settings and mathematical models used to discuss them have varied considerably from one area to another. Over the last five year…
Uniqueness theorem for extremal charged black holes in de Sitter space.
problem Proving uniqueness of extremal charged black holes in de Sitter space.
method Analyzing Einstein-Maxwell theory with a positive cosmological constant.
result Local isometry to extremal Reissner-Nordström-de Sitter black hole or its near-horizon geometry.
We study some aspects of spherical symmetric dyonic non-supersymmetric black holes in 4dN=1 supergravity coupled to chiral and vector multiplets on Kähler-Ricci solitons. Then, we have a family of dyonic non-supersymmetric black holes deformed with respect to the flow parameter related to the Kähler-Ricci soliton…
Proof of reverse isoperimetric inequality for black holes.
problem Reverse isoperimetric inequality for black holes in Einstein gravity.
method Geometric-analytic approach.
result Reversal of the usual isoperimetric inequality is explained by curved backgrounds governed by Einstein's equations.
Avoid explaining black box models; use interpretable ones instead.
problem High-stakes decisions made by black box models cause societal harm.
method Design inherently interpretable models instead of trying to explain black box models.
result Inherently interpretable models are a better approach for high-stakes decisions.
Extracts weighted automata from black box models for sequential data.
problem Global interpretability of black box models for symbolic sequential data.
method Spectral algorithm for extracting weighted automata from black boxes without access to inner representation.
result Approximation of black box models using inferred weighted automata is of high quality.
We found a new series to calculate Black-Scholes efficiently.
problem Calculating the Black-Scholes formula efficiently.
method Proved and tested a series representation for the European Black-Scholes call.
result Works in every market configuration and refines previous approximations.
Neural network learns to solve Black-Scholes for stock options.
problem Stock option pricing using the Black-Scholes Equation.
method Neural Networks applied to solve the Black-Scholes Equation.
result Neural network can accurately forecast stock option prices.
Spanning attack improves black-box attacks with unlabeled data.
problem Query inefficiency in black-box attacks due to high input space dimensionality.
method Proposes spanning attack by constraining adversarial perturbations in a low-dimensional subspace via an auxiliary unlabeled dataset.
result Significantly improves query efficiency of black-box attacks.
Distill-and-Compare audits black-box models by training transparent models to mimic them.
problem Auditing proprietary, opaque black-box risk scoring models.
method Model distillation and comparison of transparent student models to black-box models.
result Identifies missing features in black-box models, improving transparency.
This paper describes the black hole threshold in a moduli space of spherically symmetric spacetimes.
problem Understanding the black hole threshold in a moduli space of spherically symmetric spacetimes.
method Complete description and analysis of the black hole threshold in the moduli space M. result The black hole threshold is the extremal leaf of a C1 foliation of the moduli space, separating black hole solutions from non-collapsing solutions. The paper challenges the notion that asset return doesn't affect Black-Scholes-Merton model.
problem The role of asset return in the Black-Scholes-Merton model.
method Refutation of the claim through simplified stochastic calculus approach.
result The expected rate of return of the underlying asset does affect the Black-Scholes-Merton model.
The geometry of five-dimensional Kerr black holes is discussed based on geodesics and Weyl curvatures. Kerr-Star space, Star-Kerr space and Kruskal space are naturally introduced by using special null geodesics. We show that the geodesics of AdS Kerr black hole are integrable, which generalizes the result of Frolov and…
New construction of self-dual black holes using quadrics.
problem Hidden features of self-dual black holes obscured by twistor theory.
method Holomorphic quadrics in dual twistor space.
result Directly encoded geometry of self-dual black holes in quadrics.
Researchers create black holes isometric to extremal Reissner-Nordström.
problem Third law of black hole thermodynamics.
method Novel Ck characteristic gluing procedure and scalar field pulses. result Definitive disproof of the third law of black hole thermodynamics.
End-to-end training of neural networks with black-box functions.
problem Training neural networks for tasks that require precise, non-differentiable functions.
method Approximate black-box functions with differentiable neural networks and integrate them into neural network training.
result Neural network trained to compute inputs for black-box functions, generalizing better and learning more efficiently.
Topology connects to black holes and wormholes.
problem Understanding topological changes in 3D space.
method Direct connection via surgery.
result New insights into black hole and wormhole formation.
Unified approach for sequence design combining likelihood-free inference and black-box optimization.
problem Designing biological sequences efficiently and accurately.
method Unified probabilistic framework integrating likelihood-free inference and black-box optimization.
result Previous optimization methods can be adapted and new algorithms proposed within this framework.
Adds charged black holes to de Sitter space.
problem Gluing charged black holes into de Sitter space.
method Extends Hintz's result to Einstein-Maxwell system with positive cosmological constant, using Reissner-Nordström or Kerr--Newman--de Sitter black holes.
result Determines conditions for gluing black holes into de Sitter space.
Derives Black-Scholes model using central limit theorem.
problem Deriving the Black-Scholes formula for European options.
method Central limit theorem argument for undergraduate understanding.
result Elementary derivation accessible to undergraduates.
Achieved all-orders worldline action for Kerr black hole.
problem Calculating effective action for Kerr black hole.
method Twistor particle theory.
result All-orders worldline effective action for Kerr black hole.
Extreme black holes with $\SU(2)$ symmetry have a specific near horizon geometry.
problem Understanding the near horizon geometry of extreme black holes with $\SU(2)$ symmetry.
method Analyzing the near horizon geometry of 5D extreme black holes with $\SU(2)$ symmetry.
result The near horizon geometry of these black holes must be that of a Berger sphere.
Derives Black-Scholes model without stochastic calculus or PDEs.
problem Deriving the Black-Scholes model without advanced math.
method Continuum limit of Binomial tree approach.
result Derives Black-Scholes model and exchange-option generalization.
Study of waves on Reissner-Nordström-AdS black holes, proving uniform boundedness and continuity.
problem Analyzing waves on black holes in AdS spacetimes, focusing on uniform boundedness and continuity.
method Initial data on a spacelike hypersurface, Dirichlet boundary conditions at infinity, proving uniform boundedness and continuity.
result Uniform boundedness and continuity of waves at the Cauchy horizon on Reissner-Nordström-AdS black holes.
RG-2 flow reveals horizons in noncompact black hole metrics.
problem Understanding the evolution of black hole metrics under RG-2 flow.
method Adapted proofs for asymptotically flat case, analyzed horizons and monotonicity of entanglement entropy.
result Entanglement entropy is monotonic under RG-2 flow, related to horizon appearance.
New black hole models with both null and spacelike singularities.
problem Understanding singularities in black hole spacetimes.
method Developed a new spacelike-characteristic gluing method to construct black hole spacetimes.
result First examples of black holes with coexisting null and spacelike singularities.
Black holes offer insights into machine learning's loss landscapes.
problem Understanding the loss landscape in machine learning.
method Comparing machine learning loss landscapes to black hole entropy.
result Black holes provide an infinite family of potential landscapes with known minima.
Modeling stochastic arbitrage bubbles in Black-Scholes framework.
problem Analyzing arbitrage bubbles in financial markets.
method Developed a generalized Black-Scholes equation with stochastic arbitrage bubbles.
result The Black-Scholes model is a low-energy limit of a stochastic model.
Interpretable companion model for black-box classifiers.
problem Dilemma between interpretable and black-box models.
method Trains a companion model from data and black-box model predictions, optimizing a combination of accuracy and complexity.
result Companion model provides interpretable predictions with a slight accuracy loss for user choice.
The paper proposes a different method of solving a simplified version of the Black-Scholes equation. This paper will discuss the importance of the Black-Scholes equation and its applications in finance.
Learning machines can mimic the dynamics of black systems without knowing their equations.
problem Simulating black systems without knowing their equations of motion.
method Train a learning machine with input-output responses or time series of a black system.
result Learning machines can mimic the dynamics of various black systems and their evolution history.
Deep neural network predicts black hole merger remnants with high accuracy.
problem Estimating the properties of black hole merger remnants.
method Trained on a dataset of binary black hole simulations, a deep neural network predicts mass and spin with high precision.
result The network predicts remnant black hole mass and spin with errors less than 0.04% and 0.3% respectively, and reduces errors in precessing cases to half.
We analyze a generalized version of the Black-Scholes equation depending on a parameter a∈(−∞,0). It satisfies the martingale condition and coincides with the Black-Scholes equation in the limit case a↗0. We show that the generalized equation is exactly solvable in terms of Hermite polynomials a…
Study proves inequality linking black hole properties and angular momentum.
problem Establishing a Penrose-type inequality for black holes with 3-sphere horizons.
method Analyzing biaxially symmetric, maximal, asymptotically flat initial data sets for the Einstein equations.
result Equality holds only for stationary Myers-Perry black holes.
New research shows many recent defenses against adversarial examples are ineffective against black-box attacks.
problem The robustness of recent defenses against adversarial examples is insufficient, especially against black-box attacks.
method Evaluation of nine defenses on two black-box adversarial models and six attacks on CIFAR-10 and Fashion-MNIST datasets.
result Most recent defenses provide only marginal improvements in security (<25%) compared to undefended networks. Options financial instruments designed to protect investors from the stock market randomness. In 1973, Fisher Black, Myron Scholes and Robert Merton proposed a very popular option pricing method using stochastic differential equations within the Ito interpretation. Herein, we derive the Black-Scholes equation for the o…
A key result in four dimensional black hole physics, since the early 1970s, is Hawking's topology theorem asserting that the cross-sections of an "apparent horizon", separating the black hole region from the rest of the spacetime, are topologically two-spheres. Later, during the 1990s, by applying a variant of Hawking'…
New method optimizes black-box functions using generative models and Wasserstein distance.
problem Optimizing black-box functions with stochastic responses in high dimensions.
method Deep generative surrogate models and Wasserstein distance for uncertainty estimation.
result Method outperforms state-of-the-art methods in robustness to function shape and stochasticity.
Hybrid model combines interpretable and black-box models for better transparency and performance.
problem Balancing interpretability and predictive performance in machine learning models.
method Proposes a Hybrid Predictive Model (HPM) integrating an interpretable model with a black-box model, using principled objective functions and customized training algorithms.
result Hybrid models achieve an efficient trade-off between transparency and predictive performance.
Paper proposes a new black-box attack approach to minimize visual distortion.
problem Constructing adversarial examples that minimize visual distortion in a black-box threat model.
method Learning the noise distribution of adversarial examples to approximate the gradient of a non-differentiable loss function.
result The proposed attack results in much lower visual distortion compared to state-of-the-art black-box attacks.