On the Impossibility of Probabilistic Proofs in Relativized Worlds

We initiate the systematic study of probabilistic proofs in relativized worlds, where the goal is to understand, for a given oracle, the possibility of "non-trivial" proof systems for deterministic or nondeterministic computations that make queries to the oracle. This question is intimately related to a recent line of work that seeks to improve the efficiency of probabilistic proofs for computations that use functionalities such as cryptographic hash functions and digital signatures, by instantiating them via constructions that are "friendly" to known constructions of probabilistic proofs. Informally, negative results about probabilistic proofs in relativized worlds provide evidence that this line of work is inherent and, conversely, positive results provide a way to bypass it. We prove several impossibility results for probabilistic proofs relative to natural oracles. Our results provide strong evidence that tailoring certain natural functionalities to known probabilistic proofs is inherent

Distinguishing between inhomogeneous model and ΛCDM\Lambda\textrm{CDM} model with the cosmic age method

Cosmological observables could be used to construct cosmological models, however, a fixed number of observables limited on the light cone is not enough to uniquely determine a certain model. A reconstructed spherically symmetric, inhomogeneous model that share the same angular-diameter-distance-redshift relationship $d_A(z)$ and Hubble parameter $H(z)$ besides $\Lambda\textrm{CDM}$ model (which we call LTB-$\Lambda\textrm{CDM}$ model in this paper), may provide another solution. Cosmic age, which is off the light cone, could be employed to distinguish these two models. We derive the formulae for age calculation with origin conditions. From the data given by 9-year WMAP measurement, we compute the likelihood of the parameters in these two models respectively by using the Distance Prior method and do likelihood analysis by generating Monte Carlo Markov Chain for the purpose of breaking the degeneracy of $\Omega_m$ and $H_0$ (the parameters that we use for calculation). The results yield to be: $t_{\Lambda\textrm{CDM}} =13.76 \pm 0.09 ~\rm Gyr$, $t_{\rm {LTB}-\Lambda\textrm{CDM}} =11.38 \pm 0.15 ~\rm Gyr$, both in $1\sigma$ agreement with the constraint of cosmic age given by metal-deficient stars. The cosmic age method that is set in this paper enables us to distinguish between the inhomogeneous model and $\Lambda\textrm{CDM}$ model.Comment: 10 pages, 2 figures, accepted by Physics Letters B. arXiv admin note: text overlap with arXiv:0911.3852 by other author

High-Dimensional Expanders from Expanders

We present an elementary way to transform an expander graph into a simplicial complex where all high order random walks have a constant spectral gap, i.e., they converge rapidly to the stationary distribution. As an upshot, we obtain new constructions, as well as a natural probabilistic model to sample constant degree high-dimensional expanders. In particular, we show that given an expander graph G, adding self loops to G and taking the tensor product of the modified graph with a high-dimensional expander produces a new high-dimensional expander. Our proof of rapid mixing of high order random walks is based on the decomposable Markov chains framework introduced by [Jerrum et al., 2004]

Automating the Reconstruction of Neuron Morphological Models: the Rivulet Algorithm Suite

The automatic reconstruction of single neuron cells is essential to enable large-scale data-driven investigations in computational neuroscience. The problem remains an open challenge due to various imaging artefacts that are caused by the fundamental limits of light microscopic imaging. Few previous methods were able to generate satisfactory neuron reconstruction models automatically without human intervention. The manual tracing of neuron models is labour heavy and time-consuming, making the collection of large-scale neuron morphology database one of the major bottlenecks in morphological neuroscience. This thesis presents a suite of algorithms that are developed to target the challenge of automatically reconstructing neuron morphological models with minimum human intervention. We first propose the Rivulet algorithm that iteratively backtracks the neuron fibres from the termini points back to the soma centre. By refining many details of the Rivulet algorithm, we later propose the Rivulet2 algorithm which not only eliminates a few hyper-parameters but also improves the robustness against noisy images. A soma surface reconstruction method was also proposed to make the neuron models biologically plausible around the soma body. The tracing algorithms, including Rivulet and Rivulet2, normally need one or more hyper-parameters for segmenting the neuron body out of the noisy background. To make this pipeline fully automatic, we propose to use 2.5D neural network to train a model to enhance the curvilinear structures of the neuron fibres. The trained neural networks can quickly highlight the fibres of interests and suppress the noise points in the background for the neuron tracing algorithms. We evaluated the proposed methods in the data released by both the DIADEM and the BigNeuron challenge. The experimental results show that our proposed tracing algorithms achieve the state-of-the-art results

Rejection and vaccination in lung transplant recipients

This thesis addresses two pivotal issues in lung transplant recipients (LTRs): the detection of biomarkers for acute rejection (AR) and an investigation into the immunogenicity of the mRNA-1273 vaccine. Acute rejection is a significant risk following lung transplantation, prompting our focus into identifying biomarkers at both genetic and cellular levels. The study specifically focuses on T and B cell subsets associated with AR across longitudinal time points, utilizing Nanostring technology to analyze genetic expression and explore genes linked to cells and chemokines related to AR.Given the heightened susceptibility of LTRs to SARS-CoV-2 due to immunosuppressive treatments, our primary objective is to investigate the immunogenicity of the mRNA-1273 vaccine in conferring immunity against SARS-CoV-2 infection in this population. The study focus on humoral and cellular responses within LTRs compared to patients on the transplantation waiting list and control subjects. A sub-analysis is conducted on patients with a history of infection before vaccination. Additionally, an in-depth examination of T cell responses related to antibody responders enhances our understanding of the intricate interplay between humoral and cellular responses. Altogether, these identified biomarker studies can help assess the status of immunosuppression, and may serve as valuable indicators in optimizing vaccination approaches for LTRs