Computational Behavioral Models in Public Goods Games with Migration Between Groups

In this study we have simulated numerically two models of linear Public Goods Games where players are equally distributed among a given number of groups. Agents play in their group by using two simple sets of rules that are inspired by the observed behavior of human participants in laboratory experiments. In addition, unsatisfied agents have the option of leaving their group and migrating to a new random one through probabilistic choices. Stochasticity, and the introduction of two types of players in the population, help simulate the heterogeneous behavior that is often observed in experimental work. The numerical simulation results of the corresponding dynamical systems show that being able to leave a group when unsatisfied favors contribution and avoids free-riding to a good extent in a range of the enhancement factor where defection would prevail without migration. Our numerical simulation results are qualitatively in line with known experimental data when human agents are given the same kind of information about themselves and the other players in the group. This is usually not the case with customary mathematical models based on replicator dynamics or stochastic approaches. As a consequence, models like the ones described here may be useful for understanding experimental results and also for designing new experiments by first running cheap simulations instead of doing costly preliminary laboratory work. The downside is that models and their simulation tend to be less general than standard mathematical approaches.

Effectiveness of Basic Sets of Goncarov and Related Polynomials

The Chapter presents diverse but related results to the theory of the proper and generalized Goncarov polynomials. Couched in the language of basic sets theory, we present effectiveness properties of these polynomials. The results include those relating to simple sets of polynomials whose zeros lie in the closed unit disk U=z:z≤1.. They settle the conjecture of Nassif on the exact value of the Whittaker constant. Results on the proper and generalized Goncarov polynomials which employ the q-analogue of the binomial coefficients and the generalized Goncarov polynomials belonging to the Dq- derivative operator are also given. Effectiveness results of the generalizations of these sets depend on whether q<1 or q>1. The application of these and related sets to the search for the exact value of the Whittaker constant is mentioned.

Analyzing the Dual Space of the Saturated Ideal of a Regular Set and the Local Multiplicities of its Zeros

In this paper, we are concerned with the problem of counting the multiplicities of a zero-dimensional regular set’s zeros. We generalize the squarefree decomposition of univariate polynomials to the so-called pseudo squarefree decomposition of multivariate polynomials, and then propose an algorithm for decomposing a regular set into a finite number of simple sets. From the output of this algorithm, the multiplicities of zeros could be directly read out, and the real solution isolation with multiplicity can also be easily produced. As a main theoretical result of this paper, we analyze the structure of dual space of the saturated ideal generated by a simple set as well as a regular set. Experiments with a preliminary implementation show the efficiency of our method.

The Black–Scholes Equation with Impulses at Random Times Via Generalized Riemann Integral

The classical pricing theory requires that the simple sets of outcomes are extended, using the Kolmogorov Extension Theorem, to a sigma-algebra of measurable sets in an infinite-dimensional sample space whose elements are continuous paths; the process involved are represented by appropriate stochastic differential equations (using Itô calculus); a suitable measure for the sample space can be found by means of the Girsanov and Radon–Nikodym Theorems; the derivative asset valuation is determined by means of an expression using Lebesgue integration. It is known that if we replace Lebesgue’s by the generalized Riemann integration to obtain the expectation, the same result can be achieved by elementary methods. In this paper, we consider the Black–Scholes PDE subject to impulse action. We replace the process which follows a geometric Brownian motion by a process which has additional impulsive displacements at random times. Instead of constants, the volatility and the risk-free interest rate are considered as continuous functions which can vary in time. Using the Feynman–Ka[Formula: see text] formulation based on generalized Riemann integration, we obtain a pricing formula for a European call option which copes with many discontinuities. This paper seeks to develop techniques of mathematical analysis in derivative pricing theory which are less constrained by the standard assumption of lognormality of prices. Accordingly, the paper is aimed primarily at analysis rather than finance. An example is given to illustrate the main results.

Data-driven analysis of the number of Lennard-Jones types needed in a force field

<p>We optimized force fields with smaller and larger sets of chemically motivated Lennard-Jones types against the experimental properties of organic liquids. Surprisingly, we obtained results as good as or better than those from much more complex typing schemes from exceedingly simple sets of LJ types; e.g. a model with only two types of hydrogen and only one type apiece for carbon, nitrogen and oxygen.</p><p>The results justify sharply limiting the number of parameters to be optimized in future force field development work, thus reducing the risks of overfitting and the difficulties of reaching a global optimum in the multidimensional parameter space. They thus increase our chances of arriving at well-optimized force fields that will improve predictive accuracy, with applications in biomolecular modeling and computer-aided drug design. The results also prove the feasibility and value of a rigorous, data-driven approach to advancing the science of force field development.</p>

Data-driven analysis of the number of Lennard-Jones types needed in a force field

<p>We optimized force fields with smaller and larger sets of chemically motivated Lennard-Jones types against the experimental properties of organic liquids. Surprisingly, we obtained results as good as or better than those from much more complex typing schemes from exceedingly simple sets of LJ types; e.g. a model with only two types of hydrogen and only one type apiece for carbon, nitrogen and oxygen.</p><p>The results justify sharply limiting the number of parameters to be optimized in future force field development work, thus reducing the risks of overfitting and the difficulties of reaching a global optimum in the multidimensional parameter space. They thus increase our chances of arriving at well-optimized force fields that will improve predictive accuracy, with applications in biomolecular modeling and computer-aided drug design. The results also prove the feasibility and value of a rigorous, data-driven approach to advancing the science of force field development.</p>

Matching Revenues and Costs: The Counter-Intuitive Rationality of Direct Costing

This study investigates the consequences of adopting two simple sets of rules the manager can consider as perfectly rational and follow in his decisions regarding price, volume and mix of the various products. The first set follows the full (absorption) costing method logic, while the second is based on the direct (variable, marginal) costing method logic. It shows that costing systems adopting the full-costing method can lead management to make non-rational decisions regarding the setting of prices, acceptance of orders, make or buy choices and, above all, determination of the optimal production mix through programming and budgeting. On the other hand, using the direct costing method allows the manager to achieve rational results during the decision-making and planning phases, even if these often appear counter-intuitive when compared with the results achieved using the full costing method, which seem to conform to na&iuml;ve intuition. The risk in the latter case is even more serious when we are dealing with multi-production firms operating under conditions of limited production capacity regarding one or more factors, as occurs most of the time. The demonstration of the thesis of the superiority of direct costing method rules in management decisions related to the problem of the matching costs and revenues is carried out with numerical evidence, formulating a set of decision problems that are solved by comparing the results obtained both with the full costing method rules and with the direct costing method rules.

Basic operations on propositions

Chapter 3 considers what the basic operations are that can be performed on propositions in inquisitive semantics. In the classical setting, where propositions are simple sets of worlds, one can form the intersection or the union of two propositions, or the complement of a single proposition. These operations play a central role in logic and in semantic analyses of natural languages: conjunction and disjunction are standardly taken to express intersection and union, respectively, while negation is standardly taken to express complementation. It is shown that these operations have natural counterparts in the inquisitive setting, even though propositions are no longer simple sets of worlds.