We prove two recent conjectures of Liu and Wang by establishing the strong q-log-convexity of the Narayana polynomials, and showing that the Narayana transformation preserves log-convexity. We begin with a formula of Brändén expressing the q-Narayana numbers as a specialization of Schur functions and, by deriving several symmetric function identities, we obtain the necessary Schur-positivity re...

We consider trace functions (A,B) 7→ Tr[(ABA)] where A and B are positive n × n matrices and ask when these functions are convex or concave. We also consider operator convexity/concavity of ABA and convexity/concavity of the closely related trace functional Tr[ABAC]. The concavity questions are completely resolved, thereby settling cases left open by Hiai; the convexity questions are settled in...

We consider the learning problem under an online Markov decision process (MDP) aimed at learning the time-dependent decision-making policy of an agent that minimizes the regret-the difference from the best fixed policy. The difficulty of online MDP learning is that the reward function changes over time. In this letter, we show that a simple online policy gradient algorithm achieves regret O(√T)...

We construct examples for the one-phase Stefan problem which show that $$\alpha $$ -concavity of solution is in general not preserved time, $$0 \le \alpha <1/2$$ . In particular, this shows that, contrast to case heat equation a fixed convex domain, log concavity solutions problem.

Many trace inequalities can be expressed either as concavity/convexity theorems or monotonicity theorems. A classic example is the joint convexity of quantum relative entropy which equivalent to Data Processing Inequality. The latter says that operations never increase entropy. versions often have many advantages, and direct physical application, in just mentioned. Moreover, results are valid f...

Identifying a protein's functional sites is an important step towards characterizing its molecular function. Numerous structure- and sequence-based methods have been developed for this problem. Here we introduce ConCavity, a small molecule binding site prediction algorithm that integrates evolutionary sequence conservation estimates with structure-based methods for identifying protein surface c...

OBJECTIVES To study the prevalence and the degree of lingual concavity in the edentulous first molar region from cone beam computed tomography (CBCT) scans of the mandibles. MATERIAL AND METHODS Qualified cross-sectional images in mandibular first molar edentulous region taken from CBCT were selected. The mandible morphology 2 mm above the inferior alveolar canal (IAC) was classified into the...