An improved algorithm for the shallow water equations model reduction: Dynamic Mode Decomposition vs POD

We propose an improved framework for dynamic mode decomposition (DMD) of 2‐D flows for problems originating from meteorology when a large time step acts like a filter in obtaining the significant Koopman modes, therefore, the classic DMD method is not effective. This study is motivated by the need to further clarify the connection between Koopman modes and proper orthogonal decomposition (POD) dynamic modes. We apply DMD and POD to derive reduced order models (ROM) of the shallow water equations. Key innovations for the DMD‐based ROM introduced in this paper are the use of the Moore–Penrose pseudoinverse in the DMD computation that produced an accurate result and a novel selection method for the DMD modes and associated amplitudes and Ritz values. A quantitative comparison of the spatial modes computed from the two decompositions is performed, and a rigorous error analysis for the ROM models obtained is presented. Copyright © 2015 John Wiley & Sons, Ltd.     

The notion of motion: covariational reasoning and the limit concept

This paper investigates outcomes of building students’ intuitive understanding of a limit as a function's predicted value by examining introductory calculus students’ conceptions of limit both before and after instruction. Students’ responses suggest that while this approach is successful at reducing the common limit equals function value misconception of a limit, new misconceptions emerged in students’ responses. Analysis of students’ reasoning indicates a lack of covariational reasoning that coordinates changes in both x and y may be at the root of the emerging limit reached near x = c misconception. These results suggest that although dynamic interpretations of limit may be intuitive for many students, care must be taken to foster a dynamic conception that is both useful at the introductory calculus level and is in line with the formal notion of limit learned in advanced mathematics. In light of the findings, suggestions for adapting the pedagogical approach used in this study are provided.     

Oscillation criteria for higher‐order nonlinear dynamic equations with Laplacians and a deviating argument on time scales

In this paper, we study the n th‐order nonlinear dynamic equation with Laplacians and a deviating argument on an above‐unbounded time scale, where n ?2, New oscillation criteria are established for the cases when n is even and odd and when α  > γ ,α  = γ , and α  < γ , respectively, with α  = α ₁?α _{n  ? 1}. Copyright © 2017 John Wiley & Sons, Ltd.     

A Strategy to Design Hyperpolarized 13C Magnetic Resonance Probes Using [1‐13C]α‐Amino Acid as a Scaffold Structure

Hyperpolarization is an emerging method that dramatically enhances NMR signal intensity. As a result of their increased sensitivity, hyperpolarized (HP) NMR molecular probes can be used to perform time‐resolved spectroscopy and imaging in vitro and in vivo. It is, however, challenging to design such probes de novo. Herein, the [1‐¹³C]α‐amino acid is reported as a scaffold structure to design HP ¹³C NMR molecular probes. The [1‐¹³C]α‐amino acid can be converted to various HP ¹³C chemical probes that show sufficient chemical shift change by altering the chemical state of the α nitrogen upon interaction with the target. Several previously reported HP probes could be explained by this design principle. To demonstrate the versatility of this approach, two α‐amino‐acid‐based HP ¹³C chemical probes, sensitive to pH and Ca²⁺ ion, were developed and used to detect targets.     

Tetracyclines as a potential antiviral therapy against Crimean Congo hemorrhagic fever virus: Docking and molecular dynamic studies

Crimean-Congo Hemorrhagic Fever Virus (CCHFV) is one of the deadliest human diseases with mortality rate near 50%. Special attention should be paid to this virus since there is no approved treatment for it. On the other hand, the recent outbreak of Ebola virus which is a member of hemorrhagic fever viruses shows this group of viruses can be extremely dangerous. Previous studies have indicated that nucleoprotein of CCHFV, a pivotal protein in virus replication, is an appropriate target for antiviral drug development. The aim of this study is finding inhibitor(s) of this protein. Herein, a virtual screening procedure employing docking followed by molecular dynamic was used to identify small molecule inhibitors of the nucleoprotein from FDA-approved drugs. Regarding CCHFV, using in-silico method is a safe way to achieve its inhibitor(s) since this virus is categorized as a World Health Organization (WHO) biosafety level 4 pathogen and therefore investigation in general laboratories is restricted. In conclusion, considering docking and molecular dynamic results alongside with bioavailability of FDA-approved drugs, doxycycline and minocycline are proposed as potential inhibitors of CCHFV nucleoprotein. There is hope, this study encourage other research groups for in-vitro and in-vivo studies about the efficacy of those two medicines in CCHFV treatment.     

Bending,Curling, Rolling,and Salient Behavior of Molecular Crystals Driven by [2+2] Cycloaddition of a Styrylbenzoxazole Derivative

We report interesting photomechanical behaviors of the dynamic molecular crystals of (E )‐2‐(2,4‐dichlorostyryl)benzo[d]oxazole ( BOACl24 ). The photosalient effect of the rod‐like crystal based on a metal‐free olefin driven by photodimerization is observed. Moreover, the needle‐like crystals of BOACl24 exhibit a reversible bending away from a UV light source. The nanofibers curl easily under UV irradiation in an organogel, in which the photo‐induced rolling of a small slice occurs. This suggests that the rapid release of the accumulated strain during photodimerization may lead to a photosalient effect, and the bending or curling happens when the strain is released slowly. Notably, [2+2] cycloaddition takes place between two different conformational isomers of BOACl24 on account of the rotation of the benzoxazole ring around the C−C bond in an excited state before photodimerization. Such topo‐photochemical reaction has not been reported elsewhere.     

A stochastic portfolio optimization model with complete memory

In this article, we consider a portfolio optimization problem of the Merton’s type with complete memory over a finite time horizon. The problem is formulated as a stochastic control problem on a finite time horizon and the state evolves according to a process governed by a stochastic process with memory. The goal is to choose investment and consumption controls such that the total expected discounted utility is maximized. Under certain conditions, we derive the explicit solutions for the associated Hamilton–Jacobi–Bellman (HJB) equations in a finite-dimensional space for exponential, logarithmic, and power utility functions. For those utility functions, verification results are established to ensure that the solutions are equal to the value functions, and the optimal controls are also derived.     

Utility maximization problem with random endowment and transaction costs: when wealth may become negative

In this article, we study the problem of maximizing expected utility from the terminal wealth with proportional transaction costs and random endowment. In the context of the existence of consistent price systems, we consider the duality between the primal utility maximization problem and the dual one, which is set up on the domain of finitely additive measures. In particular, we prove duality results for utility functions supporting possibly negative values. Moreover, we construct a shadow market by the dual optimal process and consider the utility-based pricing for random endowment.     

On the construction of non-affine jump-diffusion models

We describe a method for construction of jump analogues of certain one-dimensional diffusion processes satisfying solvable stochastic differential equations. The method is based on the reduction of the original stochastic differential equations to the ones with linear diffusion coefficients, which are reducible to the associated ordinary differential equations, by using the appropriate integrating factor processes. The analogues are constructed by means of adding the jump components linearly into the reduced stochastic differential equations. We illustrate the method by constructing jump analogues of several diffusion processes and expand the notion of market price of risk to the resulting non-affine jump-diffusion models.     

Analysis of an elasto-piezoelectric system of hemivariational inequalities with thermal effects

In this paper we prove the existence and uniqueness of a weak solution for a dynamic electo-viscoelastic problem that describes a contact between a body and a foundation. We assume the body is made from thermoviscoelastic material and consider nonmonotone boundary conditions for the contact. We use recent results from the theory of hemivariational inequalities and the fixed point theory.