Kernel Bayes' rule

A nonparametric kernel-based method for realizing Bayes' rule is proposed, based on representations of probabilities in reproducing kernel Hilbert spaces. Probabilities are uniquely characterized by the mean of the canonical map to the RKHS. The prior and conditional probabilities are expressed in terms of RKHS functions of an empirical sample: no explicit parametric model is needed for these quantities. The posterior is likewise an RKHS mean of a weighted sample. The estimator for the expectation of a function of the posterior is derived, and rates of consistency are shown. Some representative applications of the kernel Bayes' rule are presented, including Baysian computation without likelihood and filtering with a nonparametric state-space model.Comment: 27 pages, 5 figure

Kernel Belief Propagation

We propose a nonparametric generalization of belief propagation, Kernel Belief Propagation (KBP), for pairwise Markov random fields. Messages are represented as functions in a reproducing kernel Hilbert space (RKHS), and message updates are simple linear operations in the RKHS. KBP makes none of the assumptions commonly required in classical BP algorithms: the variables need not arise from a finite domain or a Gaussian distribution, nor must their relations take any particular parametric form. Rather, the relations between variables are represented implicitly, and are learned nonparametrically from training data. KBP has the advantage that it may be used on any domain where kernels are defined (Rd, strings, groups), even where explicit parametric models are not known, or closed form expressions for the BP updates do not exist. The computational cost of message updates in KBP is polynomial in the training data size. We also propose a constant time approximate message update procedure by representing messages using a small number of basis functions. In experiments, we apply KBP to image denoising, depth prediction from still images, and protein configuration prediction: KBP is faster than competing classical and nonparametric approaches (by orders of magnitude, in some cases), while providing significantly more accurate results

Kernel Exponential Family Estimation via Doubly Dual Embedding

We investigate penalized maximum log-likelihood estimation for exponential family distributions whose natural parameter resides in a reproducing kernel Hilbert space. Key to our approach is a novel technique, doubly dual embedding, that avoids computation of the partition function. This technique also allows the development of a flexible sampling strategy that amortizes the cost of Monte-Carlo sampling in the inference stage. The resulting estimator can be easily generalized to kernel conditional exponential families. We establish a connection between kernel exponential family estimation and MMD-GANs, revealing a new perspective for understanding GANs. Compared to the score matching based estimators, the proposed method improves both memory and time efficiency while enjoying stronger statistical properties, such as fully capturing smoothness in its statistical convergence rate while the score matching estimator appears to saturate. Finally, we show that the proposed estimator empirically outperforms state-of-the-artComment: 22 pages, 20 figures; AISTATS 201

APQL: A process-model query language

As business process management technology matures, organisations acquire more and more business process models. The management of the resulting collections of process models poses real challenges. One of these challenges concerns model retrieval where support should be provided for the formulation and efficient execution of business process model queries. As queries based on only structural information cannot deal with all querying requirements in practice, there should be support for queries that require knowledge of process model semantics. In this paper we formally define a process model query language that is based on semantic relationships between tasks in process models and is independent of any particular process modelling notation

New Candidates for Topological Insulators : Pb-based chalcogenide series

Here, we theoretically predict that the series of Pb-based layered chalcogenides, Pb$_n$Bi$_2$Se$_{n+3}$ and Pb$_n$Sb$_2$Te$_{n+3}$, are possible new candidates for topological insulators. As $n$ increases, the phase transition from a topological insulator to a band insulator is found to occur between $n=2$ and 3 for both series. Significantly, among the new topological insulators, we found a bulk band gap of 0.40eV in PbBi$_2$Se$_4$ which is one of the largest gap topological insulators, and that Pb$_2$Sb$_2$Te$_5$ is located in the immediate vicinity of the topological phase boundary, making its topological phase easily tunable by changing external parameters such as lattice constants. Due to the three-dimensional Dirac cone at the phase boundary, massless Dirac fermions also may be easily accessible in Pb$_2$Sb$_2$Te$_5$

Interfacial Dirac Cones from Alternating Topological Invariant Superlattice Structures of Bi2Se3

When the three-dimensional topological insulators Bi2Se3 and Bi2Te3 have an interface with vacuum, i.e., a surface, they show remarkable features such as topologically protected and spin-momentum locked surface states. However, for practical applications, one often requires multiple interfaces or channels rather than a single surface. Here, for the first time, we show that an interfacial and ideal Dirac cone is realized by alternating band and topological insulators. The multichannel Dirac fermions from the superlattice structures open a new way for applications such as thermoelectric and spintronics devices. Indeed, utilizing the interfacial Dirac fermions, we also demonstrate the possible power factor improvement for thermoelectric applications.open282

The effects of protestant Christianity on the Chinese cult of ancestors as practised in the Johannesburg area.

Thesis (Ph.D.)-University of Durban-Westville, 1989.Traditional Chinese religion involves the belief in a large number of good and evil spirit beings who are arranged in a strict hierarchical order. The spirit world is a mi r r or ed existence of the world of the living and the hierarchical order is a copy of that which was observed during the Han dynasty. Even the spirit beings are portrayed in the clothing styles of that period. The Chinese tend to be eclectic and syncretistic in their religion. Their approach to the adoption of a set of beliefs may be described as supermarket shopping for religious ideas. The historical development of Buddhism, religious Taoism as well as certain of the new religious movements in Tai~an show ample evidence of attempts to syncretise rites and beliefs. The development of filial piety since the earliest period of China's history gave rise to the formalisation of behaviour towards parents and the earlier ancestors. Certain behavioural patterns became entrenched as rites which were observed even after the death of the parents. The educated class of traditional China saw the observance of such postfunerary rites as culturally educative exercises to instill family loyalty and reverence for the dead. Such rites were also used as opportunities for the bereaved to deal with their grief in a ceremonious manner. The less educated were more prone to practise such rites as the worship of the ancestors. Filial piety served as the vehicle of ancestor veneration and in the more extreme cases, ancestor worship. The study provides a number of insights related to the different attitudes of Chinese Protestants towards the cult of the ancestors which were previously not available. A reasonably strong fundamentalist attitude exists in the Protestant community which decries any ritualistic association with the ancestral cult. A large number of Protestants draw a distinction between the cultural and the religious aspects of the ancestral cult. The reverence shown to the ancestors is seen as cultural and therefore acceptable as long as reverence is interpreted as the showing of a deep respect for the dead. The churches do not show a deep understanding of the role which the cult plays in the culture of the community. The practice of filial piety continues to be observed in tandem with the parallel Biblical teachings. However, the role of filial piety as the vehicle of ancestor veneration has not been fully grasped by the majority of church leaders and even less by the members and adherents. Certain of the churches embarked on a low profile programme to combat ancestor veneration rites especially among the senior citizens in their congregations. The attendance at the two major cultic festivals by Christians ' is no longer seen as attendance or participation in a religious rite. Such visits to the graves of relatives and friends are considered as cultural and social activities completely devoid of religious implications. The researcher found that because confusion exists in the use of certain religious terms, a corresponding confusion exists in the practice of the ancestor cult by some Chinese. On the whole, the study revealed a relatively well-informed community even amongst the younger people who were locally raised and educated when certain rites such as the 'Inviting home' ceremony was mentioned. The cult of the ancestors in Johannesburg shows a traditional persistence Johannesburg. ls gaining a few thousand environs. in spite of the Protestant influences In certain instances it appears that the new momentum, especially with the influx Taiwanese Chinese into Johannesburg and in cult of a its Many of the new immigrants continue to traditional funerary rites. observe the The sympathetic attitude of the Roman Catholic church towards the veneration of Confucius and the ancestors may in fact encourage the continued observance of the cultic rites. The Chinese Protestants continue to be faced with religious and cultural issues in terms of continuity and discontinuity. The churches and their members need to consider these issues with greater intensity and urgency. Guidelines are needed for the new generation of Chinese Protestants to the age-old question: what must a Christian surrender of his culture for the sake of his faith

Effect of flow fluctuations and nonflow on elliptic flow methods

We discuss how the different estimates of elliptic flow are influenced by flow fluctuations and nonflow effects. It is explained why the event-plane method yields estimates between the two-particle correlation methods and the multiparticle correlation methods. It is argued that nonflow effects and fluctuations cannot be disentangled without other assumptions. However, we provide equations where, with reasonable assumptions about fluctuations and nonflow, all measured values of elliptic flow converge to a unique mean v_{2,PP} elliptic flow in the participant plane and, with a Gaussian assumption on eccentricity fluctuations, can be converted to the mean v_{2,RP} in the reaction plane. Thus, the 20% spread in observed elliptic flow measurements from different analysis methods is no longer mysterious.Comment: one typo in Table I correcte

Multiple Dirac fermions from a topological insulator and graphene superlattice

Graphene and three-dimensional topological insulators are well-known Dirac materials whose bulk and surface states are governed by Dirac equations. They not only show good transport properties but also carry various quanta related to the geometrical phase such as charge, spin, and valley Hall conductances. Therefore, it is a great challenge to combine the two Dirac materials together, realizing multiple Dirac fermions. By using first-principles density-functional-theory calculations, we demonstrate such a system built from topological insulator-band insulator-graphene superlattice structures. Hexagonal boron nitride is proposed as an ideal band-insulating material in gluing graphene and topological insulators, providing a good substrate for graphene and a sharp interface with a topological insulator. The power factors for p-type doping are largely enhanced due to the charge-conducting channels through multiple Dirac cones. The systems characterized by the coexistence of the topologically protected interfacial and graphene Dirac cones can pave the way for developing integrated devices for electronics, spintronics and valleytronics applications.open5