Some Order Statistics Relating to Markov Chains: An Application to Purchasing Policies

A special instance of the general problem of decision-making under uncertainty is considered. In the absence of a well-defined utility function, the following method is adopted: First, a reasonable or acceptable policy is chosen with unspecified parameters. Then, the associated decision rule is formulated; typically, these are functional transforms of appropriate state variables. Analysis is made of the outcomes produced by the rule in conjunction with the stochastic price process. Finally, some functionals of the (random) outcomes are computed with a view to obtain measures of performance of the decision rule. In each case, the derivations indicate the dependence of the measures (of performance) on the unspecified parameters. The analysis will be employed (in a later Memorandum in this series) to (a) compare alternative decision rules on the basis of a given index of performances and (b) develop a single utility function from the trade-offs between the levels of performance measured in several ways. [Likely published circa 1964.

The Decomposition Principle in Engineering Problems: Towards a Multi-Level Concept of Problem-Solving

The principal result of this report is a demonstration that systems of ordinary differential equations of engineering that are too large for the available computers can be solved by a principle of decomposition. It is shown that the systems of resulting subproblems are members of a larger class of problems. The properties of this class are investigated and conditions stated under which the solutions of the subproblems converge to those of the original problem. A measure of the interaction between the subproblems is suggested for a subsequent investigation

Capacity Expansion in Oligopoly

Imperfections of competition may be modeled in terms of stochastic dependence of the price realized by an individual firm on certain decision variables of the firm and of its competitors; or models may be constructed describing how the profits of each competitor are influenced stochastically by the price or quantity decisions of every other competitor. Models of the latter type seem to blur the distinction between what is traditionally understood as monopolistic competition and oligopoly. We shall, therefore, look for some operational definition of oligopoly, that is, a definition in terms of what firms do and how the market (if any) is closed, leading to the formation of price(s)

A Behavioral Model of Labor Supply as Related to Wage-Price-Interest Movements

The major purpose of this paper is to develop an aggregate model of interdependence of the labor, money, and product markets. As is well-known, this interdependence is due to the joint and mutual influence of the prices established in these markets. One approach is to restrict the analysis to the interactions among the observable outcomes (prices) of these markets. From a statistical viewpoint, this analysis can be performed, for example, by means of a suitable Markov model. A pure mathematical analysis can be made by applying the dynamical models due to Samuelson, Arrow, and Arrow-Enthoven. The common limitation of this latter approach (with the exception of Arrow-Enthoven) is that attention is focused only on the gross transfer characteristics of the dynamical system. However, in order to analyze the latent (that is, not directly observable) mechanism, there is unquestionably a need for behavioral assumptions. This is the approach employed in building a class of models presented below. These models have been constructed primarily with an eye to an extensive computer simulation under alternative hypotheses. We have herewith developed an aggregate model showing interdependence of the labor, money, and product markets due to the joint and mutual influence of prices established in these markets. The dominant factors in these inter-related markets are the anticipations of product price, wage rate, and rate of return on investment and the individual attitudes towards risk in capital expansion and operation. We have also developed the dynamic theory for deviations from equilibrium in terms of an excitation matrix, which determines the dynamic trend toward equilibrium

An Operational Theory of Oligopoly

The work reported in this memorandum stems from an attempt to derive operationally meaningful propositions that may be useful to the management of a firm selling an undifferentiated product in conditions of oligopoly. It avoids the game-theoretic constructs on the one hand, and the notions of reaction functions and conjectural variations on the other; it only builds the minimum necessary framework of concepts and constructs for the purposes of decision-making. Given the structure of competition (that is, who competes over what and with what means), the organization of the market (that is, the institutional setup for the consummation of a transaction), and the nature of information available to buyers and sellers, it is demonstrated that one can derive the probability distribution of demand. This demand is demand as seen from the viewpoint of the individual firm; it is parametrized by the firm\u27s own price-offerings. The distribution, so derived, is further refined so as to be applicable in the derivation of the optimal level and course of price-setting. The level is relevant for the short-run decisions, while the course is relevant to the long-run decisions stretching over more than one period

The Decomposition Principle in Engineering Problems: Towards a Multi-Level Concept of Problem Solving

In a previous report it was shown that a large system of differential equations could be decomposed into smaller groups (called subproblems) such that the solutions of the subproblems converged to the solution of the original system. It was also shown that the decomposition was most effective when the original problem was decomposed along the boundaries of weakest interaction in terms of the Lipschitz constants. This last fact, however, is a desirable but not essential condition. The major purpose of the present report is to develop certain techniques which will facilitate the application of the decomposition principle as stated in Tech Memo No. 14. The techniques fall into two categories: (a) those that help indicate how the grouping may be done in a natural and efficient manner, and (b) those that lead to a prior simplification of the original problem before the variables are grouped. Techniques of the first category make use of what has been called directed graphs ; those of the second category concentrate on the various types of linearization

Attack Graph Generation and Analysis Techniques

As computer networks are emerging in everyday life, network security has become an important issue. Simultaneously, attacks are becoming more sophisticated, making the defense of computer networks increasingly difficult. Attack graph is a modeling tool used in the assessment of security of enterprise networks. Since its introduction a considerable amount of research effort has been spent in the development of theory and practices around the idea of attack graph. This paper presents a consolidated view of major attack graph generation and analysis techniques

An Approach to Evaluate the Profitability of Component Commonality

Commonality or the use of same components (parts, assemblies, or subsystems) among multiple products can reduce component inventory and simplify processes and logistics while accommodating variations in product demand. Excessive commonality, however, causes some products to use high-performance components and increase product cost. This paper presents an approach for evaluating profitability of component commonality by integrating commonality and supply chain decisions. The proposed approach is demonstrated using commonality of electric-bicycle motors as an illustrative example. This paper presents a sensitivity analysis of the optimum commonality with respect to motor cost, demand variability, inventory-tracking cost, and inventory-ordering cost

Regulation of Oxidized Base Repair in Human Chromatin by Posttranslational Modification

Base excision repair (BER) is the major pathway for the repair of oxidized bases and apurinic/apyrimidinic (abasic; AP) sites produced by reaction with reactive oxygen/nitrogen species (ROS/RNS). These metabolites are generated spontaneously by endogenous cellular processes and also by environmental agents. Because most of these lesions are promutagenic, linked to diverse disease-associated somatic mutations, as well as heritable single nucleotide polymorphisms (SNPs) in the normal human population, their prompt repair is warranted. Impairment of repair leading to mutation, a hallmark of cancer, underscores the essentiality of BER for maintaining genome integrity in humans and other mammals. In mammals, repair of oxidized bases and other BER substrates is initiated by DNA glycosylases (DGs), which excise the damaged bases and cleave the DNA strands at the resulting AP sites, followed by sequential end processing, gap-filling DNA synthesis, and ligation. In vitro BER performed with naked DNA substrates has been extensively studied, which delineates its basic mechanistic steps and subpathways. However, recent interest is directed to unraveling BER in cell chromatin, including its regulation via posttranslational modifications (PTMs), which occurs possibly in concert with nucleosome remodeling. Emerging reports on various PTMs of BER enzymes indicate that the PTMs, while dispensable for the enzymatic activity, regulate overall repair by modulating interactions with other repair proteins and chromatin factors, assembly of BER complexes, as well as turnover of the proteins, and may ultimately dictate the cellular phenotype. Here, we discuss recent advances in the BER field by reviewing the PTMs and how they regulate BER in chromatin

Development of an Innovative Telerehabilitation System to Improve Handgrip Strength

Handgrip strength is an essential function of the hand to perform day-to-day tasks. People lose grip strength due to various factors such as aging, diseases, and other medical conditions. According to neuroplastic principles, grip strength can be improved using goal-oriented tasks or exercises repeatedly and consistently. People often fail to adhere to meaningless repeated movements, including grip strength exercises. Studies have shown that game-based rehabilitation has improved exercise compliance and functional outcomes. This article explains the design and development of an affordable smartphone-based telerehabilitation system that include an innovatively designed grip strength device (eGripper) and a phone application to play games