Recent years have seen increasing attention and significant progress in many-light rendering, a class of methods for the efficient computation of global illumination. The many-light formulation offers a unified mathematical framework for the problem reducing the full lighting transport simulation to the calculation of the direct illumination from many virtual light sources. These methods are un...

This paper aims at building a unified framework to deal with a wide class of local and nonlocal translation-invariant geometric flows. We introduce a class of nonlocal generalized mean curvatures and prove the existence and uniqueness for the level set formulation of the corresponding geometric flows. We then introduce a class of generalized perimeters, whose first variation is an admissible ge...

In summer 1923, a year after his lectures on the ‘New Foundation of Mathematics’ and half a year before the republication of his two notes on the ‘Foundations of Physics,’ Hilbert delivered a trilogy of lectures in Hamburg. In these lectures, Hilbert expounds in an unusually explicit manner his epistemological perspective on science as a subdiscipline of an all embracing science of mathematics....

Missing values are endemic in the data sets available to econometricians. This paper suggests a unified likelihood-based approach to deal with several nonignorable missing data problems for discrete choice models. Our concern is when either the dependent variable is unobserved or situations when both dependent variable and covariates are missing for some sampling units. These cases are also con...

Under appropriate conditions, the dynamics of a control system governed by ordinary differential equations can be formulated several ways: differential inclusion, control parameterization, flatness parameterization, higher-order inclusions and so on. A plethora of techniques have been proposed for each of these formulations but they are typically not portable across equivalent mathematical form...

A generalised niche-assembly/dispersal-assembly theory is outlined. The aim is an explanatory theory of island/sample species abundance curves, of species-area curves, and of island biogeography phenomena. A niche space is defined over a spatial domain in terms of, for example, a stratification obtained from an environmental variable defined over that domain. Within each niche a neutral individ...

The coin package implements a unified approach for conditional inference procedures commonly known as permutation tests. The theoretical basis of design and implementation is the unified framework for permutation tests given by Strasser and Weber (1999). For a very flexible formulation of multivariate linear statistics, Strasser and Weber (1999) derived the conditional expectation and covarianc...

(Supervised and Unsupervised STratified Adaptive IncrementalNetwork) is a network model of human category learning. SUSTAIN initially assumes a simple category structure. If simple solutions prove inadequate and SUSTAIN is confronted with a surprising event (e.g. it is told that a bat is a mammal instead of a bird), SUSTAIN recruits an additional cluster to represent the surprising event. Newly...

The fundamental notion of bisimulation has inspired various notions of system equivalences in concurrency theory. Many notions of bisimulation for various discrete systems have been recently unified in the abstract category theoretical formulation of bisimulation due to Joyal, Nielsen and Winskel. In this paper, we adopt their framework and unify the notions of bisimulation equivalences for dis...

This paper considers the problem of allocating discrete resources according to utility functions reported by potential recipients and relates this abstract problem to resource allocation in a Utility Data Center (UDC). A simple integer program formulation, which generalizes well-known knapsack problems, permits a remarkable breadth of expression while retaining clarity and analytic tractability...