Quantum Jump from Singularity to Outside of Black Hole

Considering the role of black hole singularity in quantum evolution, a resolution to the firewall paradox is presented. It is emphasized that if an observer has the singularity as a part of his spacetime, then the semi-classical evolution would be non-unitary as viewed by him. Specifically, a free-falling observer inside the black hole would have a Hilbert space with non-unitary evolution; a quantum jump for particles encountering the singularity to outside of the horizon as late Hawking radiations. The non-unitariness in the jump resembles the one in collapse of wave function, but preserves entanglements. Accordingly, we elaborate the first postulate of black hole complementarity: freely falling observers who pass through the event horizon would have non-unitary evolution, while it does not have physically measurable effects for them. Besides, no information would be lost in the singularity. Taking the modified picture into account, the firewall paradox can be resolved, respecting No Drama. A by-product of our modification is that roughly half of the entropy of the black hole is released close to the end of evaporation in the shape of very hot Hawking radiation.Comment: 7 figures, v2 more comprehensive, v3 matches the published versio

Predicting Diffusion Reach Probabilities via Representation Learning on Social Networks

Diffusion reach probability between two nodes on a network is defined as the probability of a cascade originating from one node reaching to another node. An infinite number of cascades would enable calculation of true diffusion reach probabilities between any two nodes. However, there exists only a finite number of cascades and one usually has access only to a small portion of all available cascades. In this work, we addressed the problem of estimating diffusion reach probabilities given only a limited number of cascades and partial information about underlying network structure. Our proposed strategy employs node representation learning to generate and feed node embeddings into machine learning algorithms to create models that predict diffusion reach probabilities. We provide experimental analysis using synthetically generated cascades on two real-world social networks. Results show that proposed method is superior to using values calculated from available cascades when the portion of cascades is small

On random object allocation

In this thesis, we study a linkage between object allocation problems and twosided matching markets. Our main purpose is to analyse the desirable properties such as efficiency, respect for rank and no-discrimination, and associate them with well-known stability concept. We show that any rank respecting allocation could be interpreted a stable allocation of a specific matching market. Under certain circumstances, the allocation also exhibits no-discrimination. Also, we associate our two-sided matching market derived from an object allocation problem with aggregate efficiency concept. Moreover, we provide a process that yields the PS allocatio

Expectation heterogeneity and wealth inequality

This study examines the effect of expectation heterogeneity on wealth inequality assuming that people with higher income are more optimistic about future returns of their savings, through a modified version of Krusell - Smith heterogeneous agent’s model with uninsured idiosyncratic risk and aggregate uncertainty. Our main finding is that wealth distribution is jointly determined by general equilibrium effect, individual policy functions and income mobility under heterogeneous expectations assumption. As a result, an inverse U-shape relation between wealth inequality and level of expectation heterogeneity is observe