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In my talk I will report on the work in progress. The initial idea of the project was to test available compilers of C-like languages. Our plan is the following: Choose a reasonable subset of the language to be tested. Formalize the semantics of the sub-language in AsmL. Produce tons of different programs. Using the AsmL Test tool, build test sequences for all these programs to check the correctness of the executable binary produced by the compiler. We started with a very simple fragment of the language (if, while, break, goto, simple function call). The next reasonable step is to add exceptions handling, arithmetical expressions, classes. (Joint work with Andrey Novikov.) ©2004 Microsoft Corporation. All rights reserved.

Optimal Schedules in Kiln-Drying Through Dynamic Programming

Optimal Schedules in Kiln-Drying Through Dynamic Programming

Fuel or battery consumption of unmanned aerial vehicles (UAVs) can be improved by utilizing or avoiding air currents. This thesis adopts a network modeling approach to formulate the problem of finding minimum energy flight paths. The relevant airspace is divided into small regions using a grid of nodes, inter-connected by arcs. A function, representing energy cost, is defined on every arc in terms of the solution of a constrained nonlinear program for the optimal local airspeed to fly in a given wind field. Then, shortest-path models are implemented on the network to find the optimal paths from an origin to a destination. Five models are studied and they correspond to cases of pre-planning of flight routes and dynamic updating of routes during the course of the flight. These models use three-dimensional grids of forecasted wind currents, produced by the Naval Research Laboratory's Coupled Ocean-Atmosphere Mesoscale Prediction System (COAMPS) with horizontal resolution of 1 km. One of the shortest-path models, a stochastic-dynamic model, assumes real-time measurement capabilities of the wind velocity in the vicinity of the UAV, through its GPS-INS system, and provides updated waypoints to follow after every measurement. For each model, the energy costs of the shortest-path solutions for 1000 randomized missions over a Nevada test site are simulated and compared to the energy costs of straight-line paths. For a 100 kg UAV, the dynamic model produces an average reduction of 15.1% in the energy consumption along 40 km long round trips, and an average reduction of 30.1% under windy conditions with average wind speeds larger than 15 m/s. A stochastic-dynamic model for maximum duration, solved using a heuristic algorithm, achieves an average increase of 32.2% in the flight duration for a 100 kg UAV.

Fuel or battery consumption of unmanned aerial vehicles (UAVs) can be improved by utilizing or avoiding air currents. This thesis adopts a network modeling approach to formulate the problem of finding minimum energy flight paths. The relevant airspace is divided into small regions using a grid of nodes, inter-connected by arcs. A function, representing energy cost, is defined on every arc in terms of the solution of a constrained nonlinear program for the optimal local airspeed to fly in a given wind field. Then, shortest-path models are implemented on the network to find the optimal paths from an origin to a destination. Five models are studied and they correspond to cases of pre-planning of flight routes and dynamic updating of routes during the course of the flight. These models use three-dimensional grids of forecasted wind currents, produced by the Naval Research Laboratory's Coupled Ocean-Atmosphere Mesoscale Prediction System (COAMPS) with horizontal resolution of 1 km. One of the shortest-path models, a stochastic-dynamic model, assumes real-time measurement capabilities of the wind velocity in the vicinity of the UAV, through its GPS-INS system, and provides updated waypoints to follow after every measurement. For each model, the energy costs of the shortest-path solutions for 1000 randomized missions over a Nevada test site are simulated and compared to the energy costs of straight-line paths. For a 100 kg UAV, the dynamic model produces an average reduction of 15.1% in the energy consumption along 40 km long round trips, and an average reduction of 30.1% under windy conditions with average wind speeds larger than 15 m/s. A stochastic-dynamic model for maximum duration, solved using a heuristic algorithm, achieves an average increase of 32.2% in the flight duration for a 100 kg UAV.

Conjugate point and dynamic programming

This open access book focuses on the practical application of Adaptive Dynamic Programming (ADP) in chemotherapy drug delivery, taking into account clinical variables and real-time data. ADP's ability to adapt to changing conditions and make optimal decisions in complex and uncertain situations makes it a valuable tool in addressing pressing challenges in healthcare and other fields. As optimization technology evolves, we can expect to see even more sophisticated and powerful solutions emerge.

Probabilistic Computation Tree Logic (PCTL) is a well-known modal logic which has become a standard for expressing temporal properties of finite-state Markov chains in the context of automated model checking. In this paper, we give a definition of PCTL for noncountable-space Markov chains, and we show that there is a substantial affinity between certain of its operators and problems of Dynamic Programming. After proving some uniqueness properties of the solutions to the latter, we conclude the paper with two examples to show that some recovery strategies in practical applications, which are naturally stated as reach-avoid problems, can be actually viewed as particular cases of PCTL formulas.

Includes bibliographies

In this video, I designed iphone 14 dynamic island using only html and css. This html css design is fully responsive. This iphone 14 dynamic island was made using only HTML and CSS, Javascript was not used. You can use this design for your mobile website to introduce iphone 14 dynamic island. Video Contents : 00:00 - HTML coding 06:28 - Let's add google fonts 06:50 - Adding Variables 12:00 - CSS Styles Coding 13:33 - Coding Main Design 18:00 - Iphone 14 Buttons 22:33 - Screen and Background 37:15 - Coding Notch 01:06:10 - Pallettes 01:27:43 - Fix Bugs 01:28:50 - Final Result new 1.txt file source : bit.ly/3xqLKag ♡ Subscribe → https://bit.ly/3Lf1K4A Subscriptions, good comments and likes are great support for me 😍 Don't re-upload or edit the videos on your channel. All copyrights by AsmrProg. About AsmrProg Channel : Here I upload ASMR programming tutorials related to HTML, CSS, Sass, JavaScript, React, PHP, Frameworks such as Bootstrap and more along with creative UI/UX Designs. AsmrProg is a community for web developers from all levels to learn and grow their skills in front-end and back-end web development. AsmrProg Asmr Prog ASMR Programming ASMR Coding ASMR keyboard typing ASMR web design ASMR coding html ASMR coding website No Talking ASMR No Talking Coding No Talking Programming

In this video, I designed iphone 14 dynamic island using only html and css. This html css design is fully responsive. This iphone 14 dynamic island was made using only HTML and CSS, Javascript was not used. You can use this design for your mobile website to introduce iphone 14 dynamic island. Video Contents : 00:00 - HTML coding 06:28 - Let's add google fonts 06:50 - Adding Variables 12:00 - CSS Styles Coding 13:33 - Coding Main Design 18:00 - Iphone 14 Buttons 22:33 - Screen and Background 37:15 - Coding Notch 01:06:10 - Pallettes 01:27:43 - Fix Bugs 01:28:50 - Final Result new 1.txt file source : bit.ly/3xqLKag ♡ Subscribe → https://bit.ly/3Lf1K4A Subscriptions, good comments and likes are great support for me 😍 Don't re-upload or edit the videos on your channel. All copyrights by AsmrProg. About AsmrProg Channel : Here I upload ASMR programming tutorials related to HTML, CSS, Sass, JavaScript, React, PHP, Frameworks such as Bootstrap and more along with creative UI/UX Designs. AsmrProg is a community for web developers from all levels to learn and grow their skills in front-end and back-end web development. AsmrProg Asmr Prog ASMR Programming ASMR Coding ASMR keyboard typing ASMR web design ASMR coding html ASMR coding website No Talking ASMR No Talking Coding No Talking Programming

In this video, I designed iphone 14 dynamic island using only html and css. This html css design is fully responsive. This iphone 14 dynamic island was made using only HTML and CSS, Javascript was not used. You can use this design for your mobile website to introduce iphone 14 dynamic island. Video Contents : 00:00 - HTML coding 06:28 - Let's add google fonts 06:50 - Adding Variables 12:00 - CSS Styles Coding 13:33 - Coding Main Design 18:00 - Iphone 14 Buttons 22:33 - Screen and Background 37:15 - Coding Notch 01:06:10 - Pallettes 01:27:43 - Fix Bugs 01:28:50 - Final Result new 1.txt file source : bit.ly/3xqLKag ♡ Subscribe → https://bit.ly/3Lf1K4A Subscriptions, good comments and likes are great support for me 😍 Don't re-upload or edit the videos on your channel. All copyrights by AsmrProg. About AsmrProg Channel : Here I upload ASMR programming tutorials related to HTML, CSS, Sass, JavaScript, React, PHP, Frameworks such as Bootstrap and more along with creative UI/UX Designs. AsmrProg is a community for web developers from all levels to learn and grow their skills in front-end and back-end web development. AsmrProg Asmr Prog ASMR Programming ASMR Coding ASMR keyboard typing ASMR web design ASMR coding html ASMR coding website No Talking ASMR No Talking Coding No Talking Programming

In this video, I designed iphone 14 dynamic island using only html and css. This html css design is fully responsive. This iphone 14 dynamic island was made using only HTML and CSS, Javascript was not used. You can use this design for your mobile website to introduce iphone 14 dynamic island. Video Contents : 00:00 - HTML coding 06:28 - Let's add google fonts 06:50 - Adding Variables 12:00 - CSS Styles Coding 13:33 - Coding Main Design 18:00 - Iphone 14 Buttons 22:33 - Screen and Background 37:15 - Coding Notch 01:06:10 - Pallettes 01:27:43 - Fix Bugs 01:28:50 - Final Result new 1.txt file source : bit.ly/3xqLKag ♡ Subscribe → https://bit.ly/3Lf1K4A Subscriptions, good comments and likes are great support for me 😍 Don't re-upload or edit the videos on your channel. All copyrights by AsmrProg. About AsmrProg Channel : Here I upload ASMR programming tutorials related to HTML, CSS, Sass, JavaScript, React, PHP, Frameworks such as Bootstrap and more along with creative UI/UX Designs. AsmrProg is a community for web developers from all levels to learn and grow their skills in front-end and back-end web development. AsmrProg Asmr Prog ASMR Programming ASMR Coding ASMR keyboard typing ASMR web design ASMR coding html ASMR coding website No Talking ASMR No Talking Coding No Talking Programming

In this paper, the author indicates areas of research and some interesting and significant problems which arise in the attempt to use a certain functional equation as an effective algorithm in the study of multistage decision processes.

An expository account of the theory of dynamic programming is provided. Two problems of rather simple form are considered: (1) (Optimal Allocation). We are given a resource, x, to divide into two parts, y and x-y. From y we obtain a return of g(y); from x-y a return of h(x-y). In so doing, we expend a certain amount of the original quantity and are left with a new quantity, ay + b(x-y), where 0 a, b 1. This process is now continued. The problem is to allocate at each stage so as to maximize the total return obtained over a finite or unbounded number of stages. (2) (Efficient Gold Mining). We are fortunate enough to possess two gold mines, Anaconda and Bonanza, the first of which contains an amount x of gold, while the second possesses an amount y. In addition, we have a rather delicate gold-mining machine which has the property that if used to mine gold in Anaconda, there is a probability p sub 1 that it will mine a fraction r sub 1 of the gold there and remain in working order, and a probability (1-p sub 1) that it will mine no gold and be damaged beyond repair. Similarly, Bonanza has associated the probabilities p sub 2 and (1-p sub 2) and the fraction r sub 2.

The paper establishes existence and uniqueness theorems for a class of functional equations occurring in the theory of multi-stage games.

The mathematical problem is that of minimizing the distilling plant size for an m-cascade process.

The theory of dynamic programming is applied to a class of problems involving maximization over discrete sets. The solution is made to depend on the solution of a class of functional equations.

Consideration is given to a simplified satellite trajectory problem, corresponding to a flat earth assumption, first treated by Okhotsimskii and Eneev. A numerical solution is presented based upon the functional equation technique of dynamic programming. A proof of the fundamental result in the analytic solution is given. The same computational approach can be applied to more realistic trajectory problems.

Talk by Peter Loxley from the University of New England, Armidale, Australia.  Given to the Redwood Center for Theoretical Neuroscience at UC Berkeley. Abstract Dynamic Programming with Sparse Codes: Investigating a New Computational Role for Sparse Representations of Natural Image Sequences   Dynamic programming (DP) is a general algorithmic approach used in optimal control and Markov decision processes that balances desire for low present costs with undesirability of high future costs when choosing a sequence of controls to apply over time. Recent interest in this field has grown since Google Deepmind’s algorithms have beaten humans and world-champion programs in Atari games, and games such as chess, shogi, and go. But why do these algorithms work as well as they do? In many image-based tasks, early-layer weights of trained deep neural networks often resemble neural receptive field profiles found in the mammalian visual system. From modelling efforts in the neuroscience and signal processing communities we know this architecture generates efficient (low bit-rate) representations of natural images called sparse codes. In this work, I investigate the computational role of sparse codes by applying DP to solve the optimal control problem of tracking an object (dragonfly) over a sequence of natural images. By comparing speed of learning, memory capacity, interference, generalization, and fault tolerance for different codes, I will show some distinct computational advantages of sparse codes.

A new technique was developed for designing optimal flight test inputs for aircraft parameter estimation experiments. The principles of dynamic programming were used for the design in the time domain. This approach made it possible to include realistic practical constraints on the input and output variables. A description of the new approach is presented, followed by an example for a multiple input linear model describing the lateral dynamics of a fighter aircraft. The optimal input designs produced by the new technique demonstrated improved quality and expanded capability relative to the conventional multiple input design method.

A new technique was developed for designing optimal flight test inputs for aircraft parameter estimation experiments. The principles of dynamic programming were used for the design in the time domain. This approach made it possible to include realistic practical constraints on the input and output variables. A description of the new approach is presented, followed by an example for a multiple input linear model describing the lateral dynamics of a fighter aircraft. The optimal input designs produced by the new technique demonstrated improved quality and expanded capability relative to the conventional multiple input design method.

A new technique was developed for designing optimal flight test inputs for aircraft parameter estimation experiments. The principles of dynamic programming were used for the design in the time domain. This approach made it possible to include realistic practical constraints on the input and output variables. A description of the new approach is presented, followed by an example for a multiple input linear model describing the lateral dynamics of a fighter aircraft. The optimal input designs produced by the new technique demonstrated improved quality and expanded capability relative to the conventional multiple input design method.

This thesis presents faster (in terms of worst-case running times) exact algorithms for special cases of graph problems through dynamic programming and 2-SAT programming. Dynamic programming describes the procedure of breaking down a problem recursively into overlapping subproblems, that is, subproblems with common subsubproblems. Given optimal solutions to these subproblems, the dynamic program then combines them into an optimal solution for the original problem. 2-SAT programming refers to the procedure of reducing a problem to a set of 2-SAT formulas, that is, boolean formulas in conjunctive normal form in which each clause contains at most two literals. Computing whether such a formula is satisfiable (and computing a satisfying truth assignment, if one exists) takes linear time in the formula length. Hence, when satisfying truth assignments to some 2-SAT formulas correspond to a solution of the original problem and all formulas can be computed efficiently, that is, in polynomial time in the input size of the original problem, then the original problem can be solved in polynomial time. We next describe our main results. Diameter asks for the maximal distance between any two vertices in a given undirected graph. It is arguably among the most fundamental graph parameters. We provide both positive and negative parameterized results for distance-from-triviality-type parameters and parameter combinations that were observed to be small in real-world applications. In Length-Bounded Cut, we search for a bounded-size set of edges that intersects all paths between two given vertices of at most some given length. We confirm a conjecture from the literature by providing a polynomial-time algorithm for proper interval graphs which is based on dynamic programming. k-Disjoint Shortest Paths is the problem of finding (vertex-)disjoint paths between given vertex terminals such that each of these paths is a shortest path between the respective terminals. Its complexity for constant k > 2 has been an open problem for over 20 years. Using dynamic programming, we show that k-Disjoint Shortest Paths can be solved in polynomial time for each constant k. The problem Tree Containment asks whether a phylogenetic tree T is contained in a phylogenetic network N. A phylogenetic network (or tree) is a leaf-labeled single-source directed acyclic graph (or tree) in which each vertex has in-degree at most one or out-degree at most one. The problem stems from computational biology in the context of the tree of life (the history of speciation). We introduce a particular variant that resembles certain types of uncertainty in the input. We show that if each leaf label occurs at most twice in a phylogenetic tree N, then the problem can be solved in polynomial time and if labels can occur up to three times, then the problem becomes NP-hard. Lastly, Reachable Object is the problem of deciding whether there is a sequence of rational trades of objects among agents such that a given agent can obtain a certain object. A rational trade is a swap of objects between two agents where both agents profit from the swap, that is, they receive objects they prefer over the objects they trade away. This problem can be seen as a natural generalization of the well-known and well-studied Housing Market problem where the agents are arranged in a graph and only neighboring agents can trade objects. We prove a dichotomy result that states that the problem is polynomial-time solvable if each agent prefers at most two objects over its initially held object and it is NP-hard if each agent prefers at most three objects over its initially held object. We also provide a polynomial-time 2-SAT program for the case where the graph of agents is a cycle.

This article is from Biomedical Optics Express , volume 3 . Abstract This paper presents a generalized framework for segmenting closed-contour anatomical and pathological features using graph theory and dynamic programming (GTDP). More specifically, the GTDP method previously developed for quantifying retinal and corneal layer thicknesses is extended to segment objects such as cells and cysts. The presented technique relies on a transform that maps closed-contour features in the Cartesian domain into lines in the quasi-polar domain. The features of interest are then segmented as layers via GTDP. Application of this method to segment closed-contour features in several ophthalmic image types is shown. Quantitative validation experiments for retinal pigmented epithelium cell segmentation in confocal fluorescence microscopy images attests to the accuracy of the presented technique.

This article is from Biomedical Optics Express , volume 3 . Abstract This paper presents a generalized framework for segmenting closed-contour anatomical and pathological features using graph theory and dynamic programming (GTDP). More specifically, the GTDP method previously developed for quantifying retinal and corneal layer thicknesses is extended to segment objects such as cells and cysts. The presented technique relies on a transform that maps closed-contour features in the Cartesian domain into lines in the quasi-polar domain. The features of interest are then segmented as layers via GTDP. Application of this method to segment closed-contour features in several ophthalmic image types is shown. Quantitative validation experiments for retinal pigmented epithelium cell segmentation in confocal fluorescence microscopy images attests to the accuracy of the presented technique.

This study evaluates whether a reinforcement learning-based dynamic difficulty adjustment (RL-DDA) system can optimise cognitive load and improve programming task performance in novice learners. A within-subjects experimental design was employed with 45 undergraduate students. Each participant completed a pretest, engaged with the RL-DDA system, and then completed a posttest. The system used a Q-learning agent to adapt task difficulty based on learner performance, recalibrated every four tasks. Outcomes were measured using a validated 28-item rubric grounded in Bloom’s taxonomy, covering programming logic, problem-solving, creativity, and critical thinking. The study contributes empirical evidence on scalable adaptive systems for programming education.

Core PHP Programming, Second Edition is the first complete, practical guide to PHP 4 for experienced Web developers. Fully updated to reflect PHP 4.0's breakthrough features and performance, it covers every technique you need to build robust, fast Web applications. Leading PHP developer Leon Atkinson starts with a high-level overview of PHP: how it evolved, and how it appears to the developer. Next, Atkinson reviews the key building blocks of PHP scripts, including variables, operators, and expressions; conditional branches and loops. Review every PHP function, including I/O, data, and math functions; time, date, configuration, database, graphics, and network functions. Core PHP Programming, Second Edition also contains detailed coverage of effective program design and debugging. For all Web developers and system administrators.

We prove in a dynamic programming framework that uniform convergence of the finite horizon values implies that asymptotically the average accumulated payoff is constant on optimal trajectories. We analyze and discuss several possible extensions to two-person games.

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The aim of this paper is to announce the release of a novel system for abstract argumentation which is based on decomposition and dynamic programming. We provide first experimental evaluations to show the feasibility of this approach.

We conduct a theoretical study of various solution methods for the adaptive fractionation problem. The two messages of this paper are: (i) dynamic programming (DP) is a useful framework for adaptive radiation therapy, particularly adaptive fractionation, because it allows us to assess how close to optimal different methods are, and (ii) heuristic methods proposed in this paper are near-optimal, and therefore, can be used to evaluate the best possible benefit of using an adaptive fraction size. The essence of adaptive fractionation is to increase the fraction size when the tumor and organ-at-risk (OAR) are far apart (a "favorable" anatomy) and to decrease the fraction size when they are close together. Given that a fixed prescribed dose must be delivered to the tumor over the course of the treatment, such an approach results in a lower cumulative dose to the OAR when compared to that resulting from standard fractionation. We first establish a benchmark by using the DP algorithm to solve the problem exactly. In this case, we characterize the structure of an optimal policy, which provides guidance for our choice of heuristics. We develop two intuitive, numerically near-optimal heuristic policies, which could be used for more complex, high-dimensional problems. Furthermore, one of the heuristics requires only a statistic of the motion probability distribution, making it a reasonable method for use in a realistic setting. Numerically, we find that the amount of decrease in dose to the OAR can vary significantly (5 - 85%) depending on the amount of motion in the anatomy, the number of fractions, and the range of fraction sizes allowed. In general, the decrease in dose to the OAR is more pronounced when: (i) we have a high probability of large tumor-OAR distances, (ii) we use many fractions (as in a hyper-fractionated setting), and (iii) we allow large daily fraction size deviations.

This thesis proposes new methods, based on dynamic programming, for solving certain single-stage and multi-stage integer stochastic knapsack problems. These problems model stochastic portfolio optimization problems (SPOPs) which assume deterministic unit weight, and normally distributed unit return with known mean and variance for each item type. Given an initial wealth, the objective is to select a portfolio that maximizes the probability of achieving or exceeding a specified final return threshold; the multi-stage problem allows revisions of the portfolio at regular time intervals. An exact method is developed to solve a single-stage SPOP with independence of returns among item types. For a problem from the literature with 11 item types, this method obtains an optimal solution in a fraction of a second on a laptop computer. An approximation method, based on discretization of possible wealth values, is developed to solve a multi-stage SPOP with inter- and intra-stage independence of returns among item types. Running on a desktop computer, this approximation method solves a 3-stage problem with 6 item types in under 12 minutes. With finer discretization in a 3-stage problem with 8 item types, the solution time is about 46 minutes.

This thesis proposes new methods, based on dynamic programming, for solving certain single-stage and multi-stage integer stochastic knapsack problems. These problems model stochastic portfolio optimization problems (SPOPs) which assume deterministic unit weight, and normally distributed unit return with known mean and variance for each item type. Given an initial wealth, the objective is to select a portfolio that maximizes the probability of achieving or exceeding a specified final return threshold; the multi-stage problem allows revisions of the portfolio at regular time intervals. An exact method is developed to solve a single-stage SPOP with independence of returns among item types. For a problem from the literature with 11 item types, this method obtains an optimal solution in a fraction of a second on a laptop computer. An approximation method, based on discretization of possible wealth values, is developed to solve a multi-stage SPOP with inter- and intra-stage independence of returns among item types. Running on a desktop computer, this approximation method solves a 3-stage problem with 6 item types in under 12 minutes. With finer discretization in a 3-stage problem with 8 item types, the solution time is about 46 minutes.

This thesis proposes new methods, based on dynamic programming, for solving certain single-stage and multi-stage integer stochastic knapsack problems. These problems model stochastic portfolio optimization problems (SPOPs) which assume deterministic unit weight, and normally distributed unit return with known mean and variance for each item type. Given an initial wealth, the objective is to select a portfolio that maximizes the probability of achieving or exceeding a specified final return threshold; the multi-stage problem allows revisions of the portfolio at regular time intervals. An exact method is developed to solve a single-stage SPOP with independence of returns among item types. For a problem from the literature with 11 item types, this method obtains an optimal solution in a fraction of a second on a laptop computer. An approximation method, based on discretization of possible wealth values, is developed to solve a multi-stage SPOP with inter- and intra-stage independence of returns among item types. Running on a desktop computer, this approximation method solves a 3-stage problem with 6 item types in under 12 minutes. With finer discretization in a 3-stage problem with 8 item types, the solution time is about 46 minutes.

This thesis proposes new methods, based on dynamic programming, for solving certain single-stage and multi-stage integer stochastic knapsack problems. These problems model stochastic portfolio optimization problems (SPOPs) which assume deterministic unit weight, and normally distributed unit return with known mean and variance for each item type. Given an initial wealth, the objective is to select a portfolio that maximizes the probability of achieving or exceeding a specified final return threshold; the multi-stage problem allows revisions of the portfolio at regular time intervals. An exact method is developed to solve a single-stage SPOP with independence of returns among item types. For a problem from the literature with 11 item types, this method obtains an optimal solution in a fraction of a second on a laptop computer. An approximation method, based on discretization of possible wealth values, is developed to solve a multi-stage SPOP with inter- and intra-stage independence of returns among item types. Running on a desktop computer, this approximation method solves a 3-stage problem with 6 item types in under 12 minutes. With finer discretization in a 3-stage problem with 8 item types, the solution time is about 46 minutes.

This thesis presents an analytic procedure to derive rules for managing a conjunctive use system. In this thesis, system management refers to the specification of optimal controls: decisions regarding the release and allocation of water. The procedure is applied to a proposed conjunctive use system of practical interest, where the facilities have predetermined characteristics and where control decisions are affected by uncertain autocorrelated inputs. Optimal decisions are determined by applying the optimization method of gradient dynamic programming to a numerical model of the conjunctive use system. The resulting optimal decisions demonstrate that application of the analytic procedure can greatly improve the management of a conjunctive use system. These decisions are significantly more efficient than those that result from application of heuristic rules. Also, the analytic procedure incorporates the effect of autocorrelation, and the resulting optimal decisions demonstrate that autocorrelation is important in the control of conjunctive use systems because of the different capabilities and constraints that surface reservoir storage and aquifer storage present.

Dynamic programming is used in many military and industrial applications to solve sequential decision making problems. This research proposes the development of a model and approach to address the application of dynamic programming in nation-building modeling. Through the creation of component indices to capture the state of operational variables: Political, Military, Economic, Social, Infrastructure, and Information (PMESII), a functional form of a system of differential equations is developed to account for the interactions between the state indices and instruments of national power: Diplomatic, Informational, Military, and Economic (DIME). Solving this problem with dynamic programming provides an improved sequence which describes the application of DIME in a manner that minimizes an objective (i.e. cost, time) and allows the model to account for external factors such as an insurgent reaction to US policy. An application of the model is derived for Iraq to demonstrate the utility of the model and explore various aspects of the solution space. This modeling approach offers a potential significant capability when analyzing and planning for nation-building operations.

The major goals of this thesis were to develop a user friendly software package for processing influence diagrams, and to implement in software the extensions necessary for dynamic programming without special action or knowledge on the part of the user. The final goal was to demonstrate the efficiency of the dynamic programming techniques by applying them to several example problems. A software package, AFids (AFIT influence diagram system) was developed. The system is capable of performance equivalent to the current state of the art in commercial influence diagram software. AFids incorporates the basic influence diagram operations, the separable value function extensions, and an algorithm to automatically solve any properly formed influence diagram. Separation of the value function is automatic and requires no action or special knowledge on the part of the user beyond representing the value function explicitly as a sum or product. The software uses menus, data entry screens, and graphics to provide an effective and friendly user interface. Several extensions to influence diagram theory were implemented in the AFids package including the concepts of value rounding and outcome limiting to control the combinatorial explosion encountered when processing chains of deterministic nodes. The system is cost free and available in either source or compiled form for government users. There are no restrictions on use or distribution except for commercial use. The software runs on MS-DOS compatible microcomputers and was programmed in Turbo Pascal.

In this study we introduce and test several methods to reduce the computational cost in dynamic programming algorithms for isolated word recognition systems. Three methods will be discussed in detail: (1) Pruning by preset thresholds, (2) Search based on the Branch and Bound technique, (3) Branch and Bound based search with additional pruning. Compared to conventional algorithms, Method 3 could be seen to yield a speed up of approximately a factor of 5, at no loss of recognition accuracy. The branch and bound method with pruning is also ideally suited for research oriented systems, since pruning is independent of the parametrization used (eliminates the necessity for retuning thresholds). Additional features of this method, which are of importance to maintaining the flexibility and diagnosticity needed for such a system, will be discussed.

In the present paper we show that the method of 'approximation in policy space,' developed in the theory of dynamic programming, yields monotone convergence in the calculus of variations.

This paper presents a general dynamic model of an economy and attempts to answer a number of questions dealing, for example, with the feasibility of certain time profiles of demand, the rate of substitution between economic activities taking place in different time periods, economic growth, and industrial cycles; undoubtedly there are many more applications of the general model. The solutions to the questions involve the application of linear programming to a standard Leontief input-output flow matrix and a capital building matrix. In addition the paper proposes a method which is designed to reduce computation time considerably.

This paper presents a general dynamic model of an economy and attempts to answer a number of questions dealing, for example, with the feasibility of certain time profiles of demand, the rate of substitution between economic activities taking place in different time periods, economic growth, and industrial cycles; undoubtedly there are many more applications of the general model. The solutions to the questions involve the application of linear programming to a standard Leontief input-output flow matrix and a capital building matrix. In addition the paper proposes a method which is designed to reduce computation time considerably.

This paper presents a general dynamic model of an economy and attempts to answer a number of questions dealing, for example, with the feasibility of certain time profiles of demand, the rate of substitution between economic activities taking place in different time periods, economic growth, and industrial cycles; undoubtedly there are many more applications of the general model. The solutions to the questions involve the application of linear programming to a standard Leontief input-output flow matrix and a capital building matrix. In addition the paper proposes a method which is designed to reduce computation time considerably.

In this study we introduce and test several methods to reduce the computational cost in dynamic programming algorithms for isolated word recognition systems. Three methods will be discussed in detail: (1) Pruning by preset thresholds, (2) Search based on the Branch and Bound technique, (3) Branch and Bound based search with additional pruning. Compared to conventional algorithms, Method 3 could be seen to yield a speed up of approximately a factor of 5, at no loss of recognition accuracy. The branch and bound method with pruning is also ideally suited for research oriented systems, since pruning is independent of the parametrization used (eliminates the necessity for retuning thresholds). Additional features of this method, which are of importance to maintaining the flexibility and diagnosticity needed for such a system, will be discussed.

In this study we introduce and test several methods to reduce the computational cost in dynamic programming algorithms for isolated word recognition systems. Three methods will be discussed in detail: (1) Pruning by preset thresholds, (2) Search based on the Branch and Bound technique, (3) Branch and Bound based search with additional pruning. Compared to conventional algorithms, Method 3 could be seen to yield a speed up of approximately a factor of 5, at no loss of recognition accuracy. The branch and bound method with pruning is also ideally suited for research oriented systems, since pruning is independent of the parametrization used (eliminates the necessity for retuning thresholds). Additional features of this method, which are of importance to maintaining the flexibility and diagnosticity needed for such a system, will be discussed.

A 'bottleneck problem' in the sense that the level of economic activity will be determined by the resource in shortest supply is discussed. A typical problem of the bottleneck type involving the auto industry, the steel industry and the tool industry is presented. The problem is formulated mathematically employing a discrete approximation. After a short discussion of the difficulties of this approach, a continuous approximation is advanced. Finally, the functional equation approach is applied to the theory of dynamic programming.

A discussion is given of some of the difficulties arising in multi- dimensional maximization problems and some of the special types of problems which can be treated by dynamic programming techniques. The topic of linear programming is included.

A limit theorem is presented which is valid for a general class of Markovian decision processes. The result is of interest because of the simple conditions which are imposed and the argument used.