Fundamental properties of conditional value-at-risk (CVaR), as a measure of risk with significant advantages over value-at-risk (VaR), are derived for loss distributions in finance that can involve discreetness. Such distributions are of particular importance in applications because of the prevalence of models based on scenarios and finite sampling. CVaR is able to quantify dangers beyond VaR a...

In recent decades, different definitions of conditional Rényi entropy (CRE) have been introduced. Thus, Arimoto proposed a definition that found an application in information theory, Jizba and Arimitsu proposed a definition that found an application in time series analysis and Renner-Wolf, Hayashi and Cachin proposed definitions that are suitable for cryptographic applications. However, there i...

Frank-Wolfe (FW) algorithms with linear convergence rates have recently achieved great efficiency in many applications. Garber and Meshi (2016) designed a new decomposition-invariant pairwise FW variant with favorable dependency on the domain geometry. Unfortunately it applies only to a restricted class of polytopes and cannot achieve theoretical and practical efficiency at the same time. In th...

Delay differential equations are a class of mathematical models describing various natural and engineered phenomena with delayed feedbacks in the system. Mathematical theory of delay differential equations or functional-differential equations have been developed in the second half of twentieth century to study mathematical questions from models of population biology, biochemical reactions, neur...

The best way to develop a unique identity for the National Education Debate Association (NEDA) is to debate propositions distinct from National Debate Tournament (NDT) and the Cross Examination Debate Association (CEDA). A neglected area of debate includes propositions temporally framed in the past. Yet, the present propositional categories of fact, velue, and policy can explicitly incorporate ...

We propose two algorithms for deciding if systems of Walrasian inequalities are solvable. These algorithms may serve as nonparametric tests for multiple calibration of applied general equilibrium models or they can be used to compute counterfactual equilibria in applied general equilibrium models defined by systems of Walrasian inequalities.

We present a preliminary study of the star formation distribution within three Virgo Cluster galaxies using the 24 μm Spitzer observations from the Spitzer Survey of Virgo (SPITSOV) in combination with Hα observations. The purpose of our study is to explore the relationship between the star formation distribution within galaxies and the type (and phase) of interactions experienced within the cl...

There has been much discussion of the “right to explanation” in the EU General Data Protection Regulation, and its existence, merits, and disadvantages. Implementing a right to explanation that opens the ‘black box’ of algorithmic decision-making faces major legal and technical barriers. Explaining the functionality of complex algorithmic decisionmaking systems and their rationale in specific c...

Simultaneous move games where all the player have to take their actions simultaneously are a class of games in general game playing. In this paper we analyze how UCT performs in this class of games. We argue that UCT does not converge to a Nash equilibrium in general and the situation that it converges to can be exploited. We also analyze CFR (CounterFactual Regret) and show how it can be used ...