We describe a general framework for measuring risks, where the risk measure takes values in an abstract cone. It is shown that this approach naturally includes the classical risk measures and set-valued risk measures and yields a natural definition of vector-valued risk measures. Several main constructions of risk measures are described in this abstract axiomatic framework. It is shown that the...

To meet the need of various administrative operations such as estate infrastructure planning and management, allotment and regulation of the industrial plots, establishing new estates at various locations, Geo Spatial Technology is the key solution. Geo spatial technology covers spatial dimension which facilitates to visualize outlook of industrial estates at dynamic geographical scale. The int...

We propose the concept of pseudorandom states and study their constructions, properties, and applications. Under the assumption that quantum-secure one-way functions exist, we present concrete and efficient constructions of pseudorandom states. The non-cloning theorem plays a central role in our study—it motivates the proper definition and characterizes one of the important properties of pseudo...

We present a higher-order calculus ECC which naturally combines Coquand-Huet's calculus of constructions and Martin-LL of's type theory with universes. ECC is very expressive, both for structured abstract reasoning and for program speciication and construction. In particular , the strong sum types together with the type universes provide a useful module mechanism for abstract description of mat...

Complex arrays with good aperiodic properties are characterised and it is shown how the joining of dimensions can generate sequences which retain the aperiodic properties of the parent array. For the case of 2× 2× . . .× 2 arrays we define two new notions of aperiodicity by exploiting a unitary matrix represention. In particular, we apply unitary rotations by members of a size-3 cyclic subgroup...

Faced with massive data, is it possible to trade off (statistical) risk, and (computational) space and time? This challenge lies at the heart of large-scale machine learning. Using k-means clustering as a prototypical unsupervised learning problem, we show how we can strategically summarize the data (control space) in order to trade off risk and time when data is generated by a probabilistic mo...

In this paper, we present an account of the semantics of the English temporal prepositions and some related temporal adverbials. This account aims to describe how these expressions function in English sentences, and in particular how they contribute to the truth-conditions of the sentences in which they occur. Our account will be couched at a su ciently formal level to enable us to de ne a proc...