Fairness in machine learning has predominantly been studied in static classification settings without concern for how decisions change the underlying population over time. Conventional wisdom suggests that fairness criteria promote the long-term well-being of those groups they aim to protect. We study how static fairne…
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48 results for “static criteria”
The paper optimizes designs for distinguishing between Gaussian process models.
problem Discriminating between two Gaussian process models.
method Sequential and static design criteria, including Kullback Leibler divergences and log-likelihood ratios.
result Necessary conditions for optimal design measures are provided.
Static spherically symmetric solutions to the Einstein-Euler equations with prescribed central densities are known to exist, be unique and smooth for reasonable equations of state. Some criteria are also available to decide whether solutions have finite extent (stars with a vacuum exterior) or infinite extent. In the l…
New model considers unfairness complaints to ensure multiple fairness criteria.
problem Ensuring fairness in systems that may conflict with each other.
method Data-driven model guided by unfairness complaints, supports multiple fairness criteria, and considers their incompatibilities. Stochastic and adversarial settings analyzed with efficient algorithms.
result Efficient algorithms for both stochastic and adversarial settings with competitive guarantees.
In the Cauchy problem for asymptotically flat vacuum data the solution-jets along the cylinder at space-like infinity develop in general logarithmic singularities at the critical sets at which the cylinder touches future/past null infinity. The tendency of these singularities to spread along the null generators of null…
Robo-advisors use MPC to create dynamic investment strategies.
problem Static allocation methods limit robo-advisors' effectiveness.
method Combines MPC with Hidden Markov Model and Black-Litterman for dynamic asset allocation.
result MPC-based strategies outperform static approaches in dynamic and risk-budgeting criteria.
We consider insurance derivatives depending on an external physical risk process, for example a temperature in a low dimensional climate model. We assume that this process is correlated with a tradable financial asset. We derive optimal strategies for exponential utility from terminal wealth, determine the indifference…
Noncommutative Symmetries and Stability of Black Ellipsoids in Metric--Affine and String Gravityhep-th
We construct new classes of exact solutions in metric--affine gravity (MAG) with string corrections by the antisymmetric --field. The solutions are parametrized by generic off--diagonal metrics possessing noncommutative symmetry associated to anholonomy framerelations and related nonlinear connection (N--connection)…
In the domain of machine learning, Neural Memory Networks (NMNs) have recently achieved impressive results in a variety of application areas including visual question answering, trajectory prediction, object tracking, and language modelling. However, we observe that the attention based knowledge retrieval mechanisms us…
Study classifies static potentials on 3-manifolds, proving one-dimensionality under specific conditions.
problem Classifying the dimension of static potentials on 3-manifolds.
method Analysis of relative zero sets of static potentials, using Miao and Tam's technique.
result Proves one-dimensionality of static potentials under specific conditions.
Recently ({\em Class. Quant. Grav.} {\bf 20} 625-664) the concept of {\em causal mapping} between spacetimes --essentially equivalent in this context to the {\em chronological map} one in abstract chronological spaces--, and the related notion of {\em causal structure}, have been introduced as new tools to study causal…
In this paper we introduce a completely continuous and time-variate model of the evolution of market limit orders based on the existence, uniqueness, and regularity of the solutions to a type of stochastic partial differential equations obtained in Zheng and Sowers (2012). In contrary to several models proposed and res…
New static vacuum metrics confirmed for near Euclidean boundary data.
problem Establishing sufficient conditions for near Euclidean boundary data in static vacuum metrics.
method Using new arguments from studying the conjecture for arbitrary static vacuum metrics.
result Any hypersurface in a dense subfamily is static regular.
Static vacuum extensions with prescribed Bartnik boundary data near a general static vacuum metricmath.DG
Extends static vacuum metrics with specific boundary conditions.
problem Proving the existence of static vacuum metrics with prescribed boundary data.
method Introducing static regular types (I) and (II), showing local well-posedness, and confirming Bartnik's conjecture.
result Confirms Bartnik's static vacuum extension conjecture for a broad range of boundary conditions.
We classify static manifolds which admit more than one static decomposition whenever a condition on the curvature is fullfilled. For this, we take a standard static vector field and analyze its associated one parameter family of projections onto the base. We show that the base itself is a static manifold and the warpin…
Study of 3D vacuum static spaces with specific curvature properties.
problem Classifying 3D vacuum static spaces with certain curvature conditions.
method Used generalized maximum principle to classify 3D spaces.
result Gave a complete classification of 3D complete vacuum static spaces.
New rigidity theorem on static manifolds with boundary.
problem Static metrics on manifolds with boundary.
method Obata-type rigidity theorem, sufficient geometric conditions.
result Scalar curvature map can be locally surjective at static metrics on manifolds with boundary.
Geometric inequalities for static convex domains in hyperbolic space proved.
problem Proving geometric inequalities for static convex domains in hyperbolic space.
method Using static convexity of flow hypersurfaces, new inequalities are derived.
result New family of geometric inequalities for static convex domains in hyperbolic space.
The paper classifies vacuum static spaces with harmonic curvature.
problem Classifying vacuum static spaces with harmonic curvature.
method Extending the 4-dimensional work by Kim-Shin, the paper classifies -dimensional spaces ().
result New counterexamples to the Fischer-Marsden conjecture on compact vacuum static spaces.
The paper investigates geometrical aspects of static spacetime with almost gradient Ricci solitons.
problem Geometrical properties of static spacetime with almost gradient Ricci solitons.
method Analyzing conditions and properties of static spacetime with almost gradient Ricci solitons.
result Conditions and properties of static spacetime with almost gradient Ricci solitons are determined.
The study proves geometric inequalities for static convex domains in static rotationally symmetric spaces.
problem Proving geometric inequalities for static convex domains in static rotationally symmetric spaces.
method Locally constrained curvature flow in a static rotationally symmetric space , proving graphical solutions and static convexity preservation.
result Proves weighted geometric inequalities for static convex domains close to a slice of .
In this paper, we attack the anomaly detection problem by directly modeling the data distribution with deep architectures. We propose deep structured energy based models (DSEBMs), where the energy function is the output of a deterministic deep neural network with structure. We develop novel model architectures to integ…
Proves equality in Minkowski inequality for static, flat manifolds.
problem Proving equality in Minkowski inequality for static, flat manifolds.
method Analyzes quasi-spherical metrics and static manifolds.
result Equality in Minkowski inequality achieved only by Schwarzschild space slices.
Reinforcement Learning (RL) has demonstrated a great potential for automatically solving decision-making problems in complex uncertain environments. RL proposes a computational approach that allows learning through interaction in an environment with stochastic behavior, where agents take actions to maximize some cumula…
We consider Killing vector fields on standard static space-times and obtain equations for a vector field on a standard static space-time to be Killing. We also provide a characterization of Killing vector fields on standard static space-times with compact Riemannian parts.
Proves existence of static vacuum metrics with specific boundary data.
problem Existence of static vacuum metrics with prescribed boundary data.
method Proves existence and local uniqueness of static vacuum metrics close to the Euclidean metric.
result Existence of static vacuum metrics with prescribed Bartnik boundary data.
Analyzing static solutions in Finsler gravity, extending known results.
problem Extending the analyticity of static vacuum solutions to Finsler spacetimes.
method Examining Finsler spacetimes with properties similar to static Lorentzian spacetimes.
result Finsler spacetimes with vanishing Ricci scalar are analytic.
Paper derives Riccati equation for static spaces and proves its applications.
problem Deriving Riccati equation for static spaces.
method Proving splitting theorem and connectivity of conformal boundary.
result Establishes compactness of universal covering for static triples.
We consider a continuous-time financial market that consists of securities available for dynamic trading, and securities only available for static trading. We work in a robust framework where a set of non-dominated models is given. The concept of semi-static completeness is introduced: it corresponds to having exact re…
In this paper, we study short-time existence of static flow on complete noncompact asymptotically static manifolds from the point of view that the stationary points of the evolution equations can be interpreted as static solutions of the Einstein vacuum equations with negative cosmological constant. For a static vacuum…
Study on stellar models' topology and mass using minimal surfaces.
problem Investigating the topology and mass of static stellar models.
method Analyzing stable free boundary minimal surfaces in static perfect fluid spaces.
result Proved non-existence of stable free boundary minimal surfaces and derived upper bounds for Hawking mass.
Classifies vacuum static spaces with harmonic curvature.
problem Classifying vacuum static spaces with harmonic curvature.
method Thorough classification through geometric analysis.
result Spaces are locally isometric to four types.
On the fluid ball conjecturemath.DG
Paper proves a rigidity result for static perfect fluids.
problem Proving a rigidity result for static perfect fluids.
method Robinson's divergence formula and boundary conditions.
result Rigidity result for static perfect fluids.
Existence proved for static vacuum extensions near Schwarzschild spheres.
problem Proving existence of static vacuum extensions near Schwarzschild spheres.
method Existence and local uniqueness of static vacuum extensions for Bartnik data on a sphere near a Schwarzschild sphere.
result Existence of static vacuum extensions near Schwarzschild spheres.
Paper proves rigidity of static manifolds and applies to metric extensions.
problem Detecting rotational symmetry in static systems.
method Conformal techniques and Minkowski-type inequalities.
result Proves global uniqueness of static metric extensions.
Alternative proof for static black hole uniqueness with nonpositive mass.
problem Proving static uniqueness for Kottler spacetimes with nonpositive mass.
method Alternative, more elementary proof of static uniqueness theorem.
result Alternative proof of static uniqueness for Kottler spacetimes with nonpositive mass.
The study proves unique static manifolds with positive scalar curvature and boundary.
problem Characterizing static three-manifolds with boundary and positive scalar curvature.
method Analyzing Ricci curvature bounds and quotient spaces.
result The only orientable quotient of the Nariai static manifold with boundary is the only such manifold with connected boundary under certain conditions.
We consider hedging of a contingent claim by a 'semi-static' strategy composed of a dynamic position in one asset and static (buy-and-hold) positions in other assets. We give general representations of the optimal strategy and the hedging error under the criterion of variance-optimality and provide tractable formulas u…
New mass and staticity concepts derived from weighted curvature maps.
problem Deriving mass and staticity concepts for weighted manifolds.
method Developed a weighted curvature map and its adjoint, leading to weighted mass and static metrics.
result Equivalence and uniqueness theorems for weighted static manifolds and Penrose inequality.
Study static Einstein-Maxwell space invariant by translation.
problem Classify static Einstein-Maxwell space invariant under translation.
method Analyze static Einstein-Maxwell space conformal to pseudo-Euclidean space.
result Complete classification of static Einstein-Maxwell space invariant under translation.
Community detection has long been an important yet challenging task to analyze complex networks with a focus on detecting topological structures of graph data. Essentially, real-world graph data contains various features, node and edge types which dynamically vary over time, and this invalidates most existing community…
Adapting Israel's proof of static black hole uniqueness, we show that the Schwarzschild spacetime is the only static vacuum asymptotically flat spacetime that possesses a suitably defined photon sphere.
Simple proof for sphere mass calculation.
problem Computing the ADM mass of static sphere extensions.
method Uses mass formula for static asymptotically flat manifolds.
result Validated mass formula for small spheres.
The study finds compact vacuum static spaces with positive isotropic curvature are spheres or products of a circle and sphere.
problem Characterizing compact vacuum static spaces with positive isotropic curvature.
method Proving isometric equivalence to spheres or product spaces.
result Compact vacuum static spaces with positive isotropic curvature are isometric to spheres or product spaces.
We give some general criteria of being a homeomorphism for continuous mappings of topological manifolds, as well as criteria of being a diffeomorphism for smooth mappings of smooth manifolds. As an illustration, we apply these criteria to the problems arising in two- and three-dimensional grid generation.
Static spacetimes are stable attractors in a flow equation.
problem Stability of static spacetimes with negative cosmological constant.
method New expander entropy for Ricci-harmonic flow.
result Static metrics are stable if and only if a positive mass theorem holds.
New metrics found in hyperbolic manifolds as volume-minimizers.
problem Finding critical points of volume-renormalized mass.
method Critical points of the volume-renormalized mass over asymptotically hyperbolic manifolds.
result V-static metrics are critical points of volume-renormalized mass.
Proves a Minkowski inequality for static Einstein-Maxwell space-time.
problem Understanding the photon sphere in static Einstein-Maxwell space-time.
method Inverse mean curvature flow (IMCF) approach.
result Proves a Minkowski-like inequality for asymptotically flat static Einstein-Maxwell space-time.