On the spectral distribution of large weighted random regular graphs

McKay proved that the limiting spectral measures of the ensembles of $d$-regular graphs with $N$ vertices converge to Kesten's measure as $N\to\infty$. In this paper we explore the case of weighted graphs. More precisely, given a large $d$-regular graph we assign random weights, drawn from some distribution $\mathcal{W}$, to its edges. We study the relationship between $\mathcal{W}$ and the associated limiting spectral distribution obtained by averaging over the weighted graphs. Among other results, we establish the existence of a unique `eigendistribution', i.e., a weight distribution $\mathcal{W}$ such that the associated limiting spectral distribution is a rescaling of $\mathcal{W}$. Initial investigations suggested that the eigendistribution was the semi-circle distribution, which by Wigner's Law is the limiting spectral measure for real symmetric matrices. We prove this is not the case, though the deviation between the eigendistribution and the semi-circular density is small (the first seven moments agree, and the difference in each higher moment is $O(1/d^2)$). Our analysis uses combinatorial results about closed acyclic walks in large trees, which may be of independent interest.Comment: Version 1.0, 19 page

The (Non-)Local Density of States of Electronic Excitations in Organic Semiconductors

The rational design of organic semiconductors for optoelectronic devices relies on a detailed understanding of how their molecular and morphological structure condition the energetics and dynamics of charged and excitonic states. Investigating the role of molecular architecture, conformation, orientation and packing, this work reveals mechanisms that shape the spatially resolved densities of states in organic, small-molecular and polymeric heterostructures and mesophases. The underlying computational framework combines multiscale simulations of the material morphology at atomistic and coarse-grained resolution with a long-range-polarized embedding technique to resolve the electronic structure of the molecular solid. We show that long-range electrostatic interactions tie the energetics of microscopic states to the mesoscopic structure, with a qualitative and quantitative impact on charge-carrier level profiles across organic interfaces. The computational approach provides quantitative access to the charge-density-dependent open-circuit voltage of planar heterojunctions. The derived and experimentally verified relationships between molecular orientation, architecture, level profiles and open-circuit voltage rationalize the acceptor-donor-acceptor pattern for donor materials in high-performing solar cells. Proposing a pathway for barrier-less dissociation of charge transfer states, we highlight how mesoscale fields generate charge splitting and detrapping forces in systems with finite interface roughness. The associated design rules reflect the dominant role played by lowest-energy configurations at the interface

Face Gender Classification Based on Moment Descriptors

[[abstract]]人臉辨識相關技術不僅僅能用於身份辨識上，甚至在影像及多媒體的相關應用上都能看到蹤跡。性別分類是人臉辨識中的一項分支，可以做為人臉辨識的前處理或是結合其他辨識（例如語音辨識或簽名辨識）來提升辨識效果。 辨識技術一般可概略分為三個模組，分別是前處理模組、特徵萃取模組以及分類辨識模組。我們注意到一種特徵萃取技術，動差（矩）描述子，並未曾用在性別分類領域之內。影像先經由人臉偵測擷取出人臉的部份，再利用動差（矩）描述子將人臉影像轉化為許多個特徵形成的特徵向量，最後交給分類器進行辨識。在本論文中將會介紹數種知名的動差（矩）描述子，像是Hu Moment Invariants 、Geometric Moments、Zernike Moments以及Eigenmoments應用在性別分類上的效果。 我們採用兩種不同的資料庫，第一個是我們自行收集的簡易資料庫（Simple database），包含了100張（男女各50張）人臉影像，這些影像是正面的並且有一些表情變化，但是在亮度和人臉旋轉上的變化較小。第二個資料庫是知名的FERET人臉資料庫，包含了不同人種、年齡、表情、人臉旋轉角度以及亮度變化，為了與其他的方法比較，我們使用相同的方法從中取出900張（男女各450張）正面人臉影像。根據實驗結果，使用Eigenmoments搭配SVM得到的效果最好，在簡易資料庫中的辨識率可達100%，而在FERET資料庫中的辨識率可達84.78%。[[abstract]]Gender classification could be used to improve the performance of biometric systems such as face recognition. It is not only used for identification, but also for multimedia. In the field of multimedia applications, gender classification system could display different commercial advertisements for different genders. It could also be applied on robot vision, image searching, and so on in our daily lives. Typically, recognition technology could be roughly divided into three modules, which are the pre-processing module, feature extraction and classification module. Moment descriptors are widely used in pattern analysis, but we have not seen related literature of moment descriptors in the field of gender classification. According previous studies, shape is an effective feature for gender classification. Thus, we evaluate they could deal with gender classification good. In this thesis, we experiment several well-known moment descriptors, such as Hu Moment Invariants, Geometric Moments, Zernike Moments and Eigenmoments on gender classification problem. We use two different databases. The first is a simple database collected by ourselves. It contains 100 (50 males and 50 females) face images. The second database is well-known FERET face database. We pick out 900 (450 males and 450 females) frontal face images to implement experiments. Experimental results demonstrate the feature of gender classification could be representing by moment descriptors. The classification rate up to 100 % can be achieved when we test 10 features of Eigenmoments with SVM on simple database.[[note]]碩

Face Gender Classification Based on ICA and Moment

[[abstract]]近年來生物性別辨識是個熱門的話題，在特定的管制出入口上廣泛地被應用。然而就人臉偵測技術的逐步成熟下，如何藉由偵測出的人臉來準確地判定出性別，在電腦視覺領域中依舊是項普遍感興趣的研究。 在本篇論文中，我們使用特徵矩作為性別辨識中萃取特徵的工具，並且提出一些降低特徵矩萃取出來的特徵數量技術，來達到提升辨識效果的目的。系統架構上可分前處理模組、特徵萃取模組與分類辨識模組三個模組。將資料庫的影像輸入到本系統，透過前處理模組我們利用OpenCV人臉偵測技術框出人臉之後，再由不同框架大小來切割出內部特徵、一般特徵和外部特徵。接進行各種特徵矩進行特徵萃取，如Geometric moments、Hu moments、Zernike moments、Eigenmoments、ICA moments。最後分類辨識的結果交由支持向量機（Support vector machine, SVM）作分類。 論文中採用資料庫為FERET人臉資料庫，由實驗結果顯示出，ICA moments結合SVM可得到最佳的分類結果到達86%。[[abstract]]In recent years, biological gender identification is a hot topic. It is widely applied to the entrance security. As face detection technology becomes mature, how to use it to accurately determine the gender, is a popular research in the field of computer vision. In this paper, we propose some technologies that can reduce the amount of data generated by the Moment which is used as gender identification characteristic feature extraction tool. These technologies can enhance the recognition results. This system contains pre-processing module, feature extraction module and classification identification module. The images are input to this system. The pre-processing module detects a face with OpenCV. The detection result will be segmented into different sizes for the internal, general and external features. Through various Moment processes such as Geometric moments, Zernike moments, Eigenmoments, and ICA Moments, features can be extracted. Then, we use SVM for classification. This paper uses the FERET database for the experiments. It shows that the best classification results can reach 86% by ICA Moments with SVM classification.[[note]]碩