A central problem in ranking is to design a measure for evaluation of ranking functions. In this paper we study, from a theoretical perspective, the Normalized Discounted Cumulative Gain (NDCG) which is a family of ranking measures widely used in practice. Although there are extensive empirical studies of the NDCG family, little is known about its theoretical properties. We first show that, wha...

Nonlocality without entanglement is an interesting field. A manifestation of quantum nonlocality without entanglement is the local indistinguishability of a set of orthogonal product states. In this paper we analyze the character of operators to distinguish a set of full product bases in a multi-partite system, and show that distinguishing perfectly a set of full product bases needs only local ...

The problem of distinguishability of identical particles is considered from both experimental and theoretical points ofview. It is argued that distinguishability has to be defined relative to a definite set of experiments and that the criterion by which the particies are distinguished should be specified. Faiiure to do so may cause mismatching between theory and experiment. On the theoretical l...

In this note, I define error exponents and strong converse for the tasks of distinguishability distillation dilution. These are counterparts to one-shot distillable cost, as previously defined in resource theory asymmetric distinguishability. show that they can be evaluated by semi-definite programming, establish a number their properties, bound them using Rényi relative entropies, relate each ...

In this paper we study the language of the words that, for a given language L, distinguish between pairs of different left-quotients of L. We characterize this distinguishability operation, show that its iteration has always a fixed point, and we generalize this result to operations derived from closure operators and Boolean operators. We give an upper bound for the state complexity of the dist...

In this paper we study the language of the words that, for a given language L, distinguish between pairs of different left-quotients of L. We characterize this distinguishability operation, show that its iteration has always a fixed point, and we generalize this result to operations derived from closure operators and Boolean operators. We give an upper bound for the state complexity of the dist...