The earliest galaxies seen in 21 cm line absorption

We investigate the 21 cm absorption lines produced by non-linear structures during the early stage of reionization, i.e. the starless minihalos and the dwarf galaxies. After a detailed modelling of their properties, with particular attention to the coupling physics, we determine their 21 cm absorption line profiles. The infalling gas velocity around minihalos/dwarf galaxies strongly affects the line shape, and with the low spin temperatures outside the virial radii of the systems, gives rise to horn-like line profiles. The optical depth of a dwarf galaxy is reduced for lines of sight penetrating through its HII region, and especially, a large HII region created by a dwarf galaxy with higher stellar mass and/or a top-heavy initial mass function results in an optical depth trough rather than an absorption line. We compute synthetic spectra of 21 cm forest for both high redshift quasars and radio afterglows of gamma ray bursts (GRBs). Even with the planned SKA, radio afterglows of most if not all GRBs would still be too dim to be the background sources for high resolution (1 kHz) observations, but absorption lines can be easily detected towards a high-z quasar. Broadband observation against GRB afterglows can also be used to reveal the evolving 21 cm signal from both minihalos and dwarf galaxies if there was no X-ray background or it was extremely weak, but it becomes difficult if an early X-ray background existed. Hence the 21 cm absorption could be a powerful probe of the presence/intensity of the X-ray background and the thermal history of the early universe.Comment: 18 pages, 17 figures. Accepted for publication in MNRA

Convergence of adaptive morphological filters in the context of Markov chains

A typical parameterized r-opening *r is a filter defined as a union of openings by a collection of compact, convex structuring elements, each of which is governed by a parameter vector r. It reduces to a single parameter r-opening filter by a set of structuring elements when r is a scalar sizing parameter. The parameter vector is adjusted by a set of adaptation rules according to whether the re construction Ar derived from r correctly or incorrectly passes the signal and noise grains sampled from the image. Applied to the signal-union-noise model, the optimization problem is to find the vector of r that minimizes the Mean-Absolute-Error between the filtered and ideal image processes. The adaptive r-opening filter fits into the framework of Markov processes, the adaptive parameter being the state of the process. For a single parameter r-opening filter, we proved that there exists a stationary distribution governing the parameter in the steady state and convergence is characterized in terms of the steady-state distribution. Key filter properties such as parameter mean, parameter variance, and expected error in the steady state are characterized via the stationary distribution. Steady-state behavior is compared to the optimal solution for the uniform model, for which it is possible to derive a closed-form solution for the optimal filter. We also developed the Markov adaptation system for multiparameter opening filters and provided numerical solutions to some special cases. For multiparameter r-opening filters, various adaptive models derived from various assumptions on the form of the filter have been studied. Although the state-probability increment equations can be derived from the appropriate Chapman-Kolmogorov equations, the closed-form representation of steady-state distributions is mathematically problematic due to the support geometry of the boundary states and their transitions. Therefore, numerical methods are employed to approximate for steady state probability distributions. The technique developed for conventional opening filters is also applied to bandpass opening filters. In present thesis study, the concept of signal and noise pass sets plays a central role throughout the adaptive filter analysis. The pass set reduces to the granulometric measure (or {&r}-measure) of the signal and noise grain. Optimization and adaptation are characterized in terms of the distribution of the granulometric measures for single parameter filters, or in terms of the multivariate distribution of the signal and noise pass sets. By introducing these concepts, this thesis study also provides some optimal opening filter error equations. It has been shown in the case of the uniform distribution of single sizing parameter that there is a strong agreement between the adaptive filter and optimal filter based on analytic error minimization. This agreement has been also demonstrated in various r-opening filters. Furthermore, the probabilistic interpretation has a close connection to traditional linear adaptive filter theory. The method has been applied to the classical grain separation (clutter removal) problem. *See content for correct numerical representation

Surprising Spectral Gap and Entropy Decay Estimates in Open Quantum Systems with a Large Number of Qubits

One of the major challenges in quantum information science is to control systems with a large number of qubits. Since any realistic quantum system interacts with the environment, it is important to have quantitative estimates on decoherence. The time evolution of an open quantum system can be modeled by a Lindbladian obtained by tracing out the environment degrees of freedom and performing a Born-Markov approximation. In this paper we study the spectral gap and modified logarithmic Sobolev constant of some very simple open systems given by a representation of $\mathfrak{su}(2)$ on N-qubits. Our examples fall into the class of Lindbladians admissible to the dissipative quantum Church-Turing thesis arXiv:1105.3986. In addition, our examples can also be written as Davies generators. Moreover, the main example has a dimension-dependent spectral gap at finite temperature. This is complementary to the class of Davies generators in arXiv:1409.3435, where local spectral estimates automatically imply global ones

On coloring of graphs with girth 2ℓ+12\ell+1 and without longer odd holes. odd K4K_4-subdivisions

We say that a graph $G$ has an {\em odd $K_4$-subdivision} if some subgraph of $G$ is isomorphic to a $K_4$-subdivision and whose faces are all odd holes of $G$. For a number $\ell\geq 2$, let $\mathcal{G}_{\ell}$ denote the family of graphs which have girth $2\ell+1$ and have no odd hole with length greater than $2\ell+1$. Wu, Xu and Xu conjectured that every graph in $\bigcup_{\ell\geq2}\mathcal{G}_{\ell}$ is 3-colorable. Recently, Chudnovsky et al. and Wu et al., respectively, proved that every graph in $\mathcal{G}_2$ and $\mathcal{G}_3$ is 3-colorable. In this paper, we prove that no $4$-vertex-critical graph in $\bigcup_{\ell\geq5}\mathcal{G}_{\ell}$ has an odd $K_4$-subdivision. Using this result, Chen proved that all graphs in $\bigcup_{\ell\geq5}\mathcal{G}_{\ell}$ are 3-colorable.Comment: A figure of an odd $K_4$-subdivision was adde

An analytical model of the large neutral regions during the late stage of reionization

In this paper we investigate the nature and distribution of large neutral regions during the late epoch of reionization. In the "bubble model" of reionization, the mass distribution of large ionized regions ("bubbles") during the early stage of reionization is obtained by using the excursion set model, where the ionization of a region corresponds to the first up-crossing of a barrier by random trajectories. We generalize this idea, and develop a method to predict the distribution of large scale neutral regions during the late stage of reionization, taking into account the ionizing background after the percolation of HII regions. The large scale neutral regions which we call "neutral islands" are not individual galaxies or minihalos, but larger regions where fewer galaxies formed and hence ionized later, and they are identified in the excursion set model with the first down-crossings of the island barrier. Assuming that the consumption rate of ionizing background photons is proportional to the surface area of the neutral islands, we obtained the size distribution of the neutral islands. We also take the "bubbles-in-island" effect into account by considering the conditional probability of up-crossing a bubble barrier after down-crossing the island barrier. We find that this effect is very important. An additional barrier is set to avoid islands being percolated through. We find that there is a characteristic scale for the neutral islands, while the small islands are rapidly swallowed up by the ionizing background, this characteristic scale does not change much as the reionization proceeds.Comment: 33 pages, 11 figures, accepted by The Astrophysical Journa

Infrared background signatures of the first black holes

Angular fluctuations of the Near InfraRed Background (NIRB) intensity are observed up to scales \simlt 1^{\ensuremath{^{\circ}}}. Their interpretation is challenging as even after removing the contribution from detected sources, the residual signal is $>10$ times higher than expected from distant galaxies below the detection limit and first stars. We propose here a novel interpretation in which early, intermediate mass, accreting direct collapse black holes (DCBH), which are too faint to be detected individually in current surveys, could explain the observed fluctuations. We find that a population of highly obscured (N_{\rm H}\simgt 10^{25} \rm cm^{-2}) DCBHs formed in metal-free halos with virial temperature $10^4$ K at z\simgt 12, can explain the observed level $\approx 10^{-3}$ (nW m$^{-2}$ sr$^{-1})^2$ of the 3.6 and 4.5 $\mu$m fluctuations on scales $>100''$. The signal on smaller scales is instead produced by undetected galaxies at low and intermediate redshifts. Albeit Compton-thick, at scales $\theta> 100''$ DCBHs produce a CXB (0.5-2 keV)-NIRB ($4.5 \rm \mu m$) cross-correlation signal of $\simeq 10^{-11}$ erg s$^{-1}$ cm$^{-2}$ nW m$^{-2}$ sr$^{-1}$ slightly dependent on the specific value of the absorbing gas column ($N_{\rm H} \approx 10^{25} \rm cm^{-2}$) adopted and in agreement with the recent measurements by \cite{2012arXiv1210.5302C}. At smaller scales the cross-correlation is dominated by the emission of high-mass X-ray binaries (HMXB) hosted by the same low-$z$, undetected galaxies accounting for small scale NIRB fluctuations. These results outline the great potential of the NIRB as a tool to investigate the nature of the first galaxies and black holes.Comment: 27 pages, 8 figures, accepted for publication in MNRA