Cosmological singularity theorems such as that of Hawking and Penrose assume local curvature conditions as well as global ones like the existence of a compact (achronal) slice. Here, we prove a new singularity theorem for chronological spacetimes that satisfy what we call a `past null focusing' condition. Such a condit…
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48 results for “pasting conditions”
The paper studies the past inextendibility of FLRW spacetimes using the VDR asymptote.
problem Investigating the past inextendibility of FLRW spacetimes.
method Using the volume-distance-ratio (VDR) asymptote to assess spacetime inextendibility criteria.
result Conditions for past inextendibility of FLRW spacetimes are identified.
Investment decisions shift earlier as patience decreases, with implications for pasting conditions.
problem Investment timing under decreasing impatience.
method Game-theoretic framework with continuous-time capacity expansion problem.
result Decreasing impatience leads to earlier investment decisions, but can violate smooth pasting conditions.
We discuss the behaviour of the signature index class of closed foliated bundles under the operation of cutting and pasting. Along the way we establish several index theoretic results: we define Atiyah-Patodi-Singer (APS) index classes for Dirac-type operators on foliated bundles with boundary; we prove a relative inde…
We present a simple approach to forecasting conditional probability distributions of asset returns. We work with a parsimonious specification of ordered binary choice regression that imposes a connection on sign predictability across different quantiles. The model forecasts the future conditional probability distributi…
The Finslerian extension of the Euclidean metric is proposed and studied under rigorous conditions that the associated indicatrix is regular and convex. The relativistic pseudo-Euclidean metric is extended, too. The extensions show distinct violation of the parity, so that the future-past asymmetry of the physical …
Eight different refinements of trapped surfaces are proposed, of three basic types, each intended as potential stability conditions. Minimal trapped surfaces are strictly minimal with respect to the dual expansion vector. Outer trapped surfaces have positivity of a certain curvature, related to surface gravity. Increas…
Minimal TIP and TIF found in compact spacetimes, impacting spacetime splitting.
problem Understanding the global structure of spacetimes with compact Cauchy surfaces.
method Analysis of Terminal Indecomposable Past (TIP) and Future (TIF) sets in spacetimes with compact Cauchy surfaces.
result In a spacetime with compact Cauchy surfaces, there is always at least one minimal TIP and one minimal TIF.
A singularity theorem based on asymptotic volume growth
problem Proving singularity theorems
method Introducing asymptotic volume-expansion invariants
result Proving an explicit upper bound on the time-separation from a hypersurface to its chronological past
Study optimal consumption for loss-averse agents considering past spending peaks.
problem Optimal consumption for loss-averse agents with reference to past spending maximum.
method Adopted S-shaped utility, concave envelope, HJB variational inequality, dual transform, and smooth-fit conditions.
result Obtained piecewise closed-form solutions for optimal consumption and investment control.
Reinforcement learning with sparse rewards is challenging because an agent can rarely obtain non-zero rewards and hence, gradient-based optimization of parameterized policies can be incremental and slow. Recent work demonstrated that using a memory buffer of previous successful trajectories can result in more effective…
Study shows past market trends reduce or increase correlations between futures contracts.
problem Estimating and managing risk in non-stationary futures markets.
method Applied Principal Regression Analysis (PRA) to quantify past market movements' effect on correlations.
result Past up or down 10-day trends reduce or increase instantaneous correlations, respectively.
Conditional COT-GAN predicts sequences using past data and kernel smoothing.
problem Predicting sequences given past data.
method Conditional COT-GAN with kernel smoothing.
result Improved convergence results for sequence prediction.
A new method combines regularization and generative rehearsal for continual learning.
problem Catastrophic forgetting in neural networks over past tasks.
method Uses a normalizing flow to conditionally store past task data and regularize network embeddings.
result Performs favorably compared to state-of-the-art approaches with constant memory overhead.
The paper introduces neural INGARCH models for time series of counts.
problem Analyzing time series of counts using traditional INGARCH models.
method Combining artificial neural networks with INGARCH models.
result Neural INGARCH models outperform traditional models in information loss.
The causal structure of a strongly causal spacetime is particularly well endowed. Not only does it determine the conformal spacetime geometry when the spacetime dimension n >2, as shown by Malament and Hawking-King-McCarthy (MHKM), but also the manifold dimension. The MHKM result, however, applies more generally to spa…
Many events occur in the world. Some event types are stochastically excited or inhibited---in the sense of having their probabilities elevated or decreased---by patterns in the sequence of previous events. Discovering such patterns can help us predict which type of event will happen next and when. We model streams of d…
The paper investigates the singularity and extendibility of inflationary spacetimes.
problem The existence and extendibility of initial curvature singularities in inflationary spacetimes.
method Classification and rigorous extendibility criteria derivation for quasi-de Sitter spacetimes.
result Past-eternal inflationary scenarios are most likely physically singular, except in very special initial conditions.
Proposes a method to predict responses from covariates over time.
problem Predicting responses from covariates with changing conditional distributions over time.
method Invariant Subspace Decomposition (ISD) framework that splits the conditional distribution into time-invariant and time-dependent components.
result The decomposition can be used for zero-shot and time-adaptation prediction tasks.
Recent studies show that a negative shock in stock prices will generate more volatility than a positive shock of similar magnitude. The aim of this paper is to appraise the hypothesis under which the conditional mean and the conditional variance of stock returns are asymmetric functions of past information. We compare …
New model captures time and mark inter-dependence in TPPs.
problem Limited predictive performance of conditionally independent TPP models on entangled time and mark interactions.
method Developed a multivariate TPP that models conditional inter-dependence of time and mark, using both intensity-based and intensity-free models.
result Proposed TPP models outperform conditionally independent and dependent models in standard prediction tasks.
A model for insider trading with past price dependencies.
problem Modeling insider trading with past price information.
method Functional Itô calculus for path-dependent price functions.
result Existence of equilibrium conditions for insider trading.
Degenerate backward SPDEs in domains: non-local boundary conditions and applications to financemath.PR
Backward stochastic partial differential equations of parabolic type in bounded domains are studied in the setting where the coercivity condition is not necessary satisfied and the equation can be degenerate. Some generalized solutions based on the representation theorem are suggested. In addition to problems with a st…
New method optimizes portfolio weights as functions, outperforming traditional approaches.
problem Optimizing portfolio weights in mean-variance models.
method Functional optimization approach, treating weights as functions of past values.
result Gradient-ascent algorithms can solve functional optimization problems for mean-variance portfolio management.
Develops effective adversarial attacks on probabilistic forecasting models.
problem Adversarial attacks on neural models outputting probability distributions.
method Effective generation of adversarial attacks through Monte-Carlo estimation and Bayesian conditioning.
result Demonstrates successful generation of attacks with small input perturbations.
We study an intrinsic distribution, called polar, on the space of -dimensional integral elements of the higher order contact structure on jet spaces. The main result establishes that this exterior differential system is the prolongation of a natural system of PDEs, named pasting conditions, on sections of the bundle…
Motivated by recent proposals for a de Sitter version of the AdS/CFT correspondence, we give some topological restrictions on spacetimes of de Sitter type, i.e., spacetimes with , which admit a regular past and/or future conformal boundary. For example we show that if , , is a globally hyperbolic…
Knowledge graph reasoning is a critical task in natural language processing. The task becomes more challenging on temporal knowledge graphs, where each fact is associated with a timestamp. Most existing methods focus on reasoning at past timestamps and they are not able to predict facts happening in the future. This pa…
PI-SAC agents learn predictive information to improve RL efficiency.
problem Improving sample efficiency in reinforcement learning.
method PI-SAC agents use a contrastive version of Conditional Entropy Bottleneck to learn predictive information from past and future states.
result PI-SAC agents significantly improve sample efficiency on challenging continuous control tasks.
Two problems concerning asymptotically hyperbolic manifolds with an inner boundary are studied. First, we study scalar curvature presciption with either Dirichlet or mean curvature prescription interior boundary condition. Then we apply those results to the Lichnerowicz equation with (future or past) apparent horizon i…
The paper tackles intervention generalization using factor graph models.
problem Generalizing from past experiments to novel conditions is hard due to combinatorial space of possible interventions.
method The approach is based on intervention factor models (IFMs) and factor graph models.
result Conditions for identifiability of expected outcomes of new regimes are derived.
Regularity and stability results for the level set flow via the mean curvature flow with surgerymath.DG
In this article we use the mean curvature flow with surgery to derive regularity estimates for the level set flow going past Brakke regularity in certain special conditions allowing for 2-convex regions of high density. We also show a stability result for the plane under the level set flow.
Penrose conjecture proven for specific initial data sets.
problem Proving Penrose conjecture for certain types of initial data sets.
method Used σ-inverse mean curvature flow and a monotonicity formula.
result Penrose conjecture established for 2-convex initial data sets.
We establish a Penrose-Like Inequality for general (not necessarily time symmetric) initial data sets of the Einstein equations which satisfy the dominant energy condition. More precisely, it is shown that the ADM energy is bounded below by an expression which is proportional to the square root of the area of the outer…
We introduce a method for learning the dynamics of complex nonlinear systems based on deep generative models over temporal segments of states and actions. Unlike dynamics models that operate over individual discrete timesteps, we learn the distribution over future state trajectories conditioned on past state, past acti…
Volatility conditional on price trendscond-mat.other
The influence of the past price behaviour on the realized volatility is investigated in the present article. The results show that trending (drifting) prices lead to increased (decreased) realized volatility. This ``volatility induced by trend'' constitutes a new stylized fact. The past price behaviour is measured by a…
We propose a method for feature selection that employs kernel-based measures of independence to find a subset of covariates that is maximally predictive of the response. Building on past work in kernel dimension reduction, we show how to perform feature selection via a constrained optimization problem involving the tra…
On the Penrose inequality for dust null shells in the Minkowski spacetime of arbitrary dimensiongr-qc
A particular, yet relevant, particular case of the Penrose inequality involves null shells propagating in the Minkowski spacetime. Despite previous claims in the literature, the validity of this inequality remains open. In this paper we rewrite this inequality in terms of the geometry of the surface obtained by interse…
Sparse reward problems are one of the biggest challenges in Reinforcement Learning. Goal-directed tasks are one such sparse reward problems where a reward signal is received only when the goal is reached. One promising way to train an agent to perform goal-directed tasks is to use Hindsight Learning approaches. In thes…
We prove that the perpetual American put option price of level dependent volatility model with compound Poisson jumps is convex and is the classical solution of its associated quasi-variational inequality, that it is except at the stopping boundary and that it is everywhere (i.e. the smooth pasting conditio…
Market Mill Dependence Pattern in the Stock Market: Asymmetry Structure, Nonlinear Correlations and Predictabilityphysics.soc-ph
An empirical study of joint bivariate probability distribution of two consecutive price increments for a set of stocks at time scales ranging from one minute to thirty minutes reveals asymmetric structures with respect to the axes y=0, y=x, x=0 and y=-x. All four asymmetry patterns remarkably resemble a four-blade mill…
A new spectrum recovers cobordism cut and paste groups of manifolds with boundary.
problem Defining and studying cobordism cut and paste groups of manifolds with boundary.
method Constructing a spectrum that recovers the cobordism cut and paste groups of manifolds with boundary.
result Construction of a spectrum that recovers the cobordism cut and paste groups of manifolds with boundary.
In this paper we give sufficient conditions guaranteeing the validity of the well-known minimax theorem for the lower Snell envelope with respect to a family of absolutely continuous probability measures. Such minimax results play an important role in the characterisation of arbitrage-free prices of American contingent…
Modeling a temporal process as if it is Markovian assumes the present encodes all of the process's history. When this occurs, the present captures all of the dependency between past and future. We recently showed that if one randomly samples in the space of structured processes, this is almost never the case. So, how d…
New method learns policies from past data.
problem Learning decision policies from experience.
method Fully Probabilistic Design (FPD) formalism for stochastic policy finding.
result Proposes a new approach for policy learning.
SIBRE boosts reinforcement learning convergence by rewarding improvement over past performance.
problem Improving the rate of convergence in reinforcement learning.
method SIBRE is a reward shaping approach that rewards improvement over the agent's own past performance.
result SIBRE converges faster and more stably to the optimal policy compared to baseline RL algorithms.
Circumventing the Curse of Dimensionality in Prediction: Causal Rate-Distortion for Infinite-Order Markov Processescond-mat.stat-mech
Predictive rate-distortion analysis suffers from the curse of dimensionality: clustering arbitrarily long pasts to retain information about arbitrarily long futures requires resources that typically grow exponentially with length. The challenge is compounded for infinite-order Markov processes, since conditioning on fi…
Irrespective of local conditions imposed on the metric, any extendible spacetime U has a maximal extension containing no closed causal curves outside the chronological past of U. We prove this fact and interpret it as impossibility (in classical general relativity) of the time machines, insofar as the latter are define…