Building Multifunctional Metasystems via Algorithmic Construction

ACS Nano ◽  
2021 ◽  
Vol 15 (2) ◽  
pp. 2318-2326
Author(s):  
Dayu Zhu ◽  
Zhaocheng Liu ◽  
Lakshmi Raju ◽  
Andrew S. Kim ◽  
Wenshan Cai
Keyword(s):  
Algorithmic Construction

Dynamic Portfolio Selection

2017 ◽  
pp. 116-140
Keyword(s):  
Portfolio Optimization ◽  
Asset Allocation ◽  
Piecewise Linear ◽  
Relevant Literature ◽  
Asset Price ◽  
Piecewise Linear Function ◽  
Simple Formulation ◽  
Wolfram Mathematica ◽  
Dynamic Portfolio ◽  
Algorithmic Construction

In this chapter I recognize the importance of the stochastic programming as a significant tool in financial planning. The current practice of portfolio optimization is still limited to the simple formulation of linear programming (LR) or quadratic programming (QR) type. For that reason, relevant literature on asset-liability management (ALM) model has been reviewed and two different ALM approaches are compared: first piecewise linear function; and second a nonlinear utility function. This chapter shows that the mathematical programming methodology is ready to challenge the huge problem arising from LP portfolio optimization. A special emphasis was put on the shape of the investors' payoff functions in asset price equilibrium. The results underpin our claim that the nonlinear ALM model generated better asset allocation. An algorithmic construction of ALM model is developed in Wolfram Mathematica 9.

scholarly journals Reconciliation of Gene and Species Trees

2014 ◽  
Vol 2014 ◽  
pp. 1-22 ◽  
Author(s):  
L. Y. Rusin ◽  
E. V. Lyubetskaya ◽  
K. Y. Gorbunov ◽  
V. A. Lyubetsky
Keyword(s):  
Time Scales ◽  
Gene Evolution ◽  
Single Species ◽  
Species Tree ◽  
Gene Duplications ◽  
Species Trees ◽  
Evolutionary Scenario ◽  
Algorithmic Construction ◽  
Basic Ideas ◽  
Horizontal Transfers

The first part of the paper briefly overviews the problem of gene and species trees reconciliation with the focus on defining and algorithmic construction of the evolutionary scenario. Basic ideas are discussed for the aspects of mapping definitions, costs of the mapping and evolutionary scenario, imposing time scales on a scenario, incorporating horizontal gene transfers, binarization and reconciliation of polytomous trees, and construction of species trees and scenarios. The review does not intend to cover the vast diversity of literature published on these subjects. Instead, the authors strived to overview the problem of the evolutionary scenario as a central concept in many areas of evolutionary research. The second part provides detailed mathematical proofs for the solutions of two problems: (i) inferring a gene evolution along a species tree accounting for various types of evolutionary events and (ii) trees reconciliation into a single species tree when only gene duplications and losses are allowed. All proposed algorithms have a cubic time complexity and are mathematically proved to find exact solutions. Solving algorithms for problem (ii) can be naturally extended to incorporate horizontal transfers, other evolutionary events, and time scales on the species tree.

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