Inflaton two-point correlation in the presence of a cosmic string

Precise measurements of the microwave background anisotropy have confirmed the inflationary picture of approximately scale invariant, Gaussian primordial adiabatic density perturbations. However, there are some anomalies that suggest a small violation of rotational and/or translational invariance in the mechanism that generates the primordial density fluctuations. Motivated by this we study the two-point correlation of a massless scalar (the inflaton) when the stress tensor contains the energy density from an infinitely long straight cosmic string in addition to a cosmological constant

Decoherence problem in an ekpyrotic phase

Quantum decoherence and the transition to semiclassical behavior during inflation have been extensively considered in the literature. In this paper, we use a simple model to analyze the same process in ekpyrosis. Our result is that the quantum to classical transition would not happen during an ekpyrotic phase even for superhorizon modes, and therefore the fluctuations cannot be interpreted as classical. This implies the prediction of a scale-free power spectrum in an ekpyrotic/cyclic universe model requires more inspection

Translational Invariance and the Anisotropy of the Cosmic Microwave Background

Primordial quantum fluctuations produced by inflation are conventionally assumed to be statistically homogeneous, a consequence of translational invariance. In this paper we quantify the potentially observable effects of a small violation of translational invariance during inflation, as characterized by the presence of a preferred point, line, or plane. We explore the imprint such a violation would leave on the cosmic microwave background anisotropy, and provide explicit formulas for the expected amplitudes $$ of the spherical-harmonic coefficients.Comment: Notation improve

Oncologic impact of delay between diagnosis and radical nephroureterectomy

PurposeThis study aimed to evaluate the oncological outcome of delayed surgical wait time from the diagnosis of upper tract urothelial carcinoma (UTUC) to radical nephroureterectomy (RNU).MethodsIn this multicenter retrospective study, medical records were collected between 1988 and 2021 from 18 participating Taiwanese hospitals under the Taiwan UTUC Collaboration Group. Patients were dichotomized into the early (≤90 days) and late (>90 days) surgical wait-time groups. Overall survival, disease-free survival, and bladder recurrence-free survival were calculated using the Kaplan–Meier method and multivariate Cox regression analysis. Multivariate analysis was performed using stepwise linear regression.ResultsOf the 1251 patients, 1181 (94.4%) were classifed into the early surgical wait-time group and 70 (5.6%) into the late surgical wait-time group. The median surgical wait time was 21 days, and the median follow-up was 59.5 months. Our study showed delay-time more than 90 days appeared to be associated with worse overall survival (hazard ratio [HR] 1.974, 95% confidence interval [CI] 1.166−3.343, p = 0.011), and disease-free survival (HR 1.997, 95% CI 1.137−3.507, p = 0.016). This remained as an independent prognostic factor after other confounding factors were adjusted. Age, ECOG performance status, Charlson Comorbidity Index (CCI), surgical margin, tumor location and adjuvant systemic therapy were independent prognostic factors for overall survival. Tumor location and adjuvant systemic therapy were also independent prognostic factors for disease-free survival.ConclusionsFor patients with UTUC undergoing RNU, the surgical wait time should be minimized to less than 90 days. Prolonged delay times may be associated with poor overall and disease-free survival

Deviation from Standard Inflationary Cosmology and the Problems in Ekpyrosis

There are two competing models of our universe right now. One is Big Bang with inflation cosmology. The other is the cyclic model with ekpyrotic phase in each cycle. This paper is divided into two main parts according to these two models. In the first part, we quantify the potentially observable effects of a small violation of translational invariance during inflation, as characterized by the presence of a preferred point, line, or plane. We explore the imprint such a violation would leave on the cosmic microwave background anisotropy, and provide explicit formulas for the expected amplitudes ⟨almal'm'*⟩ of the spherical-harmonic coefficients. We then provide a model and study the two-point correlation of a massless scalar (the inflaton) when the stress tensor contains the energy density from an infinitely long straight cosmic string in addition to a cosmological constant. Finally, we discuss if inflation can reconcile with the Liouville's theorem as far as the fine-tuning problem is concerned. In the second part, we find several problems in the cyclic/ekpyrotic cosmology. First of all, quantum to classical transition would not happen during an ekpyrotic phase even for superhorizon modes, and therefore the fluctuations cannot be interpreted as classical. This implies the prediction of scale-free power spectrum in ekpyrotic/cyclic universe model requires more inspection. Secondly, we find that the usual mechanism to solve fine-tuning problems is not compatible with eternal universe which contains infinitely many cycles in both direction of time. Therefore, all fine-tuning problems including the flatness problem still asks for an explanation in any generic cyclic models

Numerical and semi-analytic approaches to Sunyaev-Zeld'ovich effect

Studies of the Sunyaev-Zel’dovich (SZ) effect are reaching observational maturity, and the detailed simulations are required to interpret upcoming data. In this thesis, we present two approaches for simulating Sunyaev-Zel’dovich maps. First, we use a hydrodynamical N-body code to generate simulated maps. On the other hand, we also construct a recipe using semi-analytic formalism to simulate SZ maps, that is, calculating the SZ anisotropies directly using results from theoretical models or observations. The latter is a time-saving method, and the influence of the physical mechanism on the outputs can be easily seen since the applied models are substitutable. Although there are many advantages for the semi-analytic method, it is much less accurate than the N-body simulation. Therefore, we generate the SZ maps, of size one square degree, with numerical and semi-analytic approaches and compare them to see in what situations they are similar. We find that the simulation results of cluster properties are in agreement with theoretical model. Futhermore, we find out that the flux-limited number counts of N-body and semi-analytic maps fit surprisingly well. With these results, the semi-analytic method will be a powerful tool for model testing and to make predictions for future SZ surveys such as PLANCK, AMiBA, SZA, AMI, etc.Acknowledgements i Abstract ii 1 Introduction 1 2 preparation 4 2.1 The Sunyaev-Zel’dovich Effect . . . . . . . . . . . . . . . . . . 4 2.2 Background Cosmology . . . . . . . . . . . . . . . . . . . . . . 5 3 Simulation Method and Map-Making Technique 8 3.1 Numerical Method – N-body Simulation . . . . . . . . . . . . 8 3.1.1 Tool and Cosmological Models . . . . . . . . . . . . . . 9 3.1.2 Map-Making Technique . . . . . . . . . . . . . . . . . . 11 3.2 Semi-Analytic Approach . . . . . . . . . . . . . . . . . . . . . 13 3.2.1 The Cluster Spatial Distribution . . . . . . . . . . . . . 13 3.2.2 Cluster Model . . . . . . . . . . . . . . . . . . . . . . . 21 3.2.3 Map-Making from Semi-Analytic Method . . . . . . . . 23 4 Results and Discussion 26 4.1 Tests of N-body Simulation Results and Semi-Analytic Model 26 4.1.1 Cluster Properties . . . . . . . . . . . . . . . . . . . . 27 4.1.2 Flux-Limited Number Counts at Some Specific Redshift 35 4.2 Simulated SZ Maps . . . . . . . . . . . . . . . . . . . . . . . . 39 4.2.1 Comparison of SZ Maps Created by two different Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.2.2 Flux-Limited Number Counts from SZ maps . . . . . . 44 5 Conclusions and Future Work 51 5.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 5.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Markets with random lifetimes and private values: mean reversion and option to trade

We consider a market in which traders arrive at random times, with random private values for the single-traded asset. A trader's optimal trading decision is formulated in terms of exercising the option to trade one unit of the asset at the optimal stopping time. We solve the optimal stopping problem under the assumption that the market price follows a mean-reverting diffusion process. the model is calibrated to experimental data taken from Alton and Plott (Principles of continuous price determination in the experimental environment with flows of random arrivals and departures. Working paper, Caltech, 2010), resulting in a very good fit. In particular, the estimated long-term mean of the traded prices is close to the theoretical long-term mean at which the expected number of buys is equal to the expected number of sells. We call that value long-term competitive equilibrium, extending the concept of flow competitive equilibrium of Alton and Plott (Principles of continuous price determination in an experimental environment with flows of random arrivals and departures. Working paper, Caltech, 2010)