Classical Optimal Theory Research Articles

Application and Optimal Control for an HBV Model with Vaccination and Treatment

In this study, we formulate a model for hepatitis B virus with control strategies of newborn vaccination and treatment. Mathematical analysis is done theoretically and numerically. The results indicate that the stability of equilibria and persistence of the disease are determined by the basic reproductive number R0. Using the least squares method, the model is applied to simulate yearly new infected cases of hepatitis B in China from 2004 to 2016. Moreover, optimal control problem with newborn vaccination and treatment appearing as functions of time is analyzed by classical optimal theory. The existence of the solution to optimality system is proved, and the simulations are conducted to show the results when optimal control or current intervention is used.

Optimization on the distribution of population densities and the arrangement of urban activities

In this paper, an approximation on the distribution of population densities and the arrangement of urban activities, over a set of n locations, is derived by using the classical multiobjective optimization theory and Shannon entropy.

A complex network theory approach for optimizing contamination warning sensor location in water distribution networks

The goal of sensor placement in water networks is to detect contamination of intentional and accidental events, and to ensure safe and quality drinking water for consumers. Solving this problem as a classical optimization problem has been the focus of attention for many years. This paper presents a new modeling approach by taking into account that a water network is a complex network. Thus, the structural and dynamical complexity properties should play a role in our sensor placement problem. We model the sensor placement problem by a novel integrated approach using both the classical optimization and complex network theory. To test our modeling approach, we have considered a well-known water network with 129 nodes and 178 links which have been researched by about 20 other research groups.

Tundra Nenets consonant sandhi as coalescence

AbstractConsonant cluster simplification in Tundra Nenets coexists with other consonantal alternations, such as fricative strengthening, lenition of stops, and a variety of NC-effects, which all apply within the same phrasal domain. These processes interact with each other, suggesting an opaque ordering within the same post-lexical domain and thus presenting a challenge not only for inherently parallel theories like classical Optimality Theory, but also for the cyclic derivational approaches such as Stratal OT. We analyze all instances of Tundra Nenets cluster simplification as coalescence and show that a variety of apparently opaque alternations accompanying cluster simplification can be seen as transparent on this account. We also argue that strengthening in consonant clusters is caused by an intermediate stage where coda obstruents lose their place and turn into a glottal stop.

A Constructive Solution to the Ranking Problem in Partial Order Optimality Theory

Partial order optimality theory (PoOT) (Anttila and Cho in Lingua 104:31---56, 1998) is a conservative generalization of classical optimality theory (COT) (Prince and Smolensky in Optimality theory: constraint interaction in generative grammar, Blackwell Publishers, Malden, 1993/2004) that makes possible the modeling of free variation and quantitative regularities without any numerical parameters. Solving the ranking problem for PoOT has so far remained an outstanding problem: allowing for free variation, given a finite set of input/output pairs, i.e., a dataset, $$\Delta $$Δ that a speaker S knows to be part of some language L, how can S learn the set of all grammars G under some constraint set C compatible with $$\Delta $$Δ?. Here, allowing for free variation, given the set of all PoOT grammars GPoOT over a constraint set C , for an arbitrary $$\Delta $$Δ, I provide set-theoretic means for constructing the actual set G compatible with $$\Delta $$Δ. Specifically, I determine the set of all STRICT ORDERS of C that are compatible with $$\Delta $$Δ. As every strict total order is a strict order, our solution is applicable in both PoOT and COT, showing that the ranking problem in COT is a special instance of a more general one in PoOT.

Idempotency in Optimality Theory

Anidempotentphonological grammar maps phonotactically licit forms faithfully to themselves. This paper establishes tight sufficient conditions for idempotency in (classical) Optimality Theory. Building on Tesar (2013), these conditions are derived in two steps. First, idempotency is shown to follow from a general formal condition on the faithfulness constraints. Second, this condition is shown to hold for a variety of faithfulness constraints which naturally arise within McCarthy & Prince’s (1995) Correspondence Theory of faithfulness. This formal analysis provides an exhaustive toolkit for modelingchain shifts, which have proven recalcitrant to a constraint-based treatment.

Estimating Matching Affinity Matrix Under Low-Rank Constraints

In this paper, we address the problem of estimating transport surplus (a.k.a. matching affinity) in high dimensional optimal transport problems. Classical optimal transport theory species the matching affinity and determines the optimal joint distribution. In contrast, we study the inverse problem of estimating matching affinity based on the observation of the joint distribution, using an entropic regularization of the problem. To accommodate high dimensionality of the data, we propose a novel method that incorporates a nuclear norm regularization which effectively enforces a rank constraint on the affinity matrix. The lowrank matrix estimated in this way reveals the main factors which are relevant for matching.

Making the form fit: Repair strategies in iKalanga loanword phonology

IKalanga has borrowed extensively from English over a long period of time. The direction of borrowing is largely linked to the sociolinguistic status and role of English, which is regarded as a technologically, culturally and politically prestigious language in Africa in general and Botswana in particular. Some of the significant phonological differences between these two languages are as follows: English allows complex onsets, syllable codas and complex syllable nuclei (long vowels and diphthongs), while iKalanga, like most other Bantu languages, does not. The tense-lax distinction is phonemic in English, while in iKalanga it is not. How does iKalanga deal with these marked structures? Complex onsets and codas are repaired through vowel epenthesis, while complex syllable nuclei are simplified through glide epenthesis. Drawing insights from the constriction-based Feature Geometry (FG) model, it is shown that epenthetic vowels and glides are products of spreading. Our overall analysis employs analytical tools from classical Optimality Theory (OT), the central idea of which is that surface forms of language reflect resolutions of conflicts between competing constraints. OT provides us with descriptive terminology and a theoretical mechanism for a principled and systematic expression of the generalisations presented in this article. We demonstrate the constraint interaction that determines the phonological structure of loanwords in iKalanga.

Optimization models with economic and game theoretic applications

Optimization models have a wide range of applications in economics and game theory. This special issue of the Annals of Operations Research contains selected and refereed papers on the topic optimization models with economic and game theoretic applications. Most of the papers in this special issue were presented at the International Symposium on Applied Optimization and Game Theoretic Models (ISAOGTM13) held during January 9–11, 2013, at the Indian Statistical Institute, Delhi Centre. This International Symposiumwas designed to promote research and applications in applied optimization and game theory by bringing together leading experts and other specialists in the field around the world with young scholars. This symposium mainly focused on classical and modern optimization theory, algorithms (local and global aspects), stochastic optimization, structured optimization, as well as related topics in applied mathematics that contain applications of optimization models in economics and game theory. Around 120 participants including speakers participated in this symposium. This symposium was an event under the project optimization and reliability modeling funded by the Indian Statistical Institute. Having broad international appeal it provided an excellent opportunity to disseminate the latest major achievements and to explore new directions and perspectives, dealingwith topics of fundamental importance in applied optimization and other related sciences (economics, physics, engineering). A special session titled Professor Santosh N. Kabadi Memorial Session was organized on combinatorial optimization to recall the memory of our dear friend Professor Santosh N. Kabadi, University of New

Estimating Matching Affinity Matrix under Low-Rank Constraints

In this paper, we address the problem of estimating transport surplus (a.k.a. matching affinity) in high dimensional optimal transport problems. Classical optimal transport theory specifies the matching affinity and determines the optimal joint distribution. In contrast, we study the inverse problem of estimating matching affinity based on the observation of the joint distribution, using an entropic regularization of the problem. To accommodate high dimensionality of the data, we propose a novel method that incorporates a nuclear norm regularization which effectively enforces a rank constraint on the affinity matrix. The low-rank matrix estimated in this way reveals the main factors which are relevant for matching.

What is Reduplication? Typology and Analysis Part 1/2: The Typology of Reduplication

AbstractReduplication has played a central role in the development of phonological theories for 30 years. The introduction of Classical Optimality Theory (OT) in the 1990s sparked intensive research into the typology and analysis of reduplicative patterns, as reduplication was a key testing area both for OT and for theories critical of OT. Now, after some 20 years of research within the OT model, it is appropriate to assess the leading ideas on reduplication that have come out of this period of concentrated research. This pair of articles serves this purpose. The first article presents a typological survey of the function and form of reduplication, covering classic forms of reduplication as well as less well‐studied forms, such as phrasal reduplication, morphologically‐complex reduplicants, and reduplication without phonological identity. The second article surveys recent formal approaches, such as Base‐Reduplicant Correspondence and Morphological Doubling, covering debates such as the morphological status of the reduplicant, exfixation, semantically empty, a‐templatic, and compensatory reduplication.

What is Reduplication? Typology and Analysis Part 2/2: The Analysis of Reduplication

AbstractReduplication has played a central role in the development of phonological theories for 30 years. The introduction of the classical optimality theory (OT) in the 1990s sparked intensive research into the typology and analysis of reduplicative patterns, as reduplication was a key testing area both for OT and for theories critical of OT. Now, after some 20 years of research within the OT model, it is appropriate to assess the leading ideas on reduplication that have come out of this period of concentrated research. This pair of articles serves this purpose. The first article presents a typological survey of the function and form of reduplication, covering classic forms of reduplication as well as less well‐studied forms, such as phrasal reduplication, morphologically complex reduplicants and reduplication without phonological identity. The second article surveys recent formal approaches, such as base‐reduplicant correspondence and morphological doubling, covering debates such as the morphological status of the reduplicant, exfixation, semantically empty, and a‐templatic and compensatory reduplication.

Stem Storage? Not Proven: A Reply to Bermúdez-Otero 2013

Stem Storage? Not Proven: A Reply to Bermúdez-Otero 2013

QoS-Compliant Sequential Channel Sensing for Cognitive Radios

In this paper, we study the quality-of-service (QoS) support for realtime traffic in cognitive radio (CR) networks when spectrum availability and quality is not known a priori. A resource-constrained CR relies on sequential channel sensing and probing to resolve spectrum uncertainty and search for good transmission opportunities in real time. We are interested in maximizing the effective throughput the CR can achieve with a desired confidence (success probability) under a spectrum access delay constraint. This quantity can be interpreted as the QoS-compliant (e.g., min-rate and delay) capacity of the CR link under the uncertain spectrum environment. The optimization is formulated as a finite-horizon optimal stopping problem under the objective of maximizing a given percentile of the rate of return at the stopping time. This formulation cannot be directly solved by classical optimal stopping theory, because the latter only supports a mean-reward objective function. A novel transformation is developed to convert the problem into solving a series of sub problems, each of which optimizes a transformed mean-reward of the original problem and therefore can be solved using classical optimal stopping method. We prove the monotonicity of the sub problems, based on which we develop a fast algorithm to efficiently find the unique solution to the original problem. To account for different MAC mechanisms used in practice, our analysis considers both non-recall and recall channel decision strategies. Extensive simulations are performed to verify the effectiveness and significance of the optimization. We show that significant gains (e.g., over 30%) on the QoS-compliant capacity can be achieved by the proposed algorithm when compared with the counterparts.

Improving real-time estimation of heavy-to-extreme precipitation using rain gauge data via conditional bias-penalized optimal estimation

Summary A new technique for gauge-only precipitation analysis for improved estimation of heavy-to-extreme precipitation is described and evaluated. The technique is based on a novel extension of classical optimal linear estimation theory in which, in addition to error variance, Type-II conditional bias (CB) is explicitly minimized. When cast in the form of well-known kriging, the methodology yields a new kriging estimator, referred to as CB-penalized kriging (CBPK). CBPK, however, tends to yield negative estimates in areas of no or light precipitation. To address this, an extension of CBPK, referred to herein as extended conditional bias penalized kriging (ECBPK), has been developed which combines the CBPK estimate with a trivial estimate of zero precipitation. To evaluate ECBPK, we carried out real-world and synthetic experiments in which ECBPK and the gauge-only precipitation analysis procedure used in the NWS’s Multisensor Precipitation Estimator (MPE) were compared for estimation of point precipitation and mean areal precipitation (MAP), respectively. The results indicate that ECBPK improves hourly gauge-only estimation of heavy-to-extreme precipitation significantly. The improvement is particularly large for estimation of MAP for a range of combinations of basin size and rain gauge network density. This paper describes the technique, summarizes the results and shares ideas for future research.

Portfolio optimization under convex incentive schemes

We consider the terminal wealth utility maximization problem from the point of view of a portfolio manager who is paid by an incentive scheme, which is given as a convex function $g$ of the terminal wealth. The manager's own utility function $U$ is assumed to be smooth and strictly concave, however the resulting utility function $U \circ g$ fails to be concave. As a consequence, the problem considered here does not fit into the classical portfolio optimization theory. Using duality theory, we prove wealth-independent existence and uniqueness of the optimal portfolio in general (incomplete) semimartingale markets as long as the unique optimizer of the dual problem has a continuous law. In many cases, this existence and uniqueness result is independent of the incentive scheme and depends only on the structure of the set of equivalent local martingale measures. As examples, we discuss (complete) one-dimensional models as well as (incomplete) lognormal mixture and popular stochastic volatility models. We also provide a detailed analysis of the case where the unique optimizer of the dual problem does not have a continuous law, leading to optimization problems whose solvability by duality methods depends on the initial wealth of the investor.

Long-Run Savings and Investment Strategy Optimization

We focus on automatic strategies to optimize life cycle savings and investment. Classical optimal savings theory establishes that, given the level of risk aversion, a saver would keep the same relative amount invested in risky assets at any given time. We show that, when optimizing lifecycle investment, performance and risk assessment have to take into account the investor's risk aversion and the maximum amount the investor could lose, simultaneously. When risk aversion and maximum possible loss are considered jointly, an optimal savings strategy is obtained, which follows from constant rather than relative absolute risk aversion. This result is fundamental to prove that if risk aversion and the maximum possible loss are both high, then holding a constant amount invested in the risky asset is optimal for a standard lifetime saving/pension process and outperforms some other simple strategies. Performance comparisons are based on downside risk-adjusted equivalence that is used in our illustration.

On the Robust Optimal Stopping Problem

We study a robust optimal stopping problem with respect to a set ${\cal P}$ of mutually singular probabilities. This can be interpreted as a zero-sum controller-stopper game in which the stopper is trying to maximize its payoff while an adverse player wants to minimize this payoff by choosing an evaluation criteria from ${\cal P}$. We show that the upper Snell envelope $\overline{Z}$ of the reward process $Y$ is a supermartingale with respect to an appropriately defined nonlinear expectation $\underline{\mathscr{E}}$, and $\overline{Z}$ is further an $\underline{\mathscr{E}}$-martingale up to the first time $\tau^*$ when $\overline{Z}$ meets $Y$. Consequently, $\tau^*$ is the optimal stopping time for the robust optimal stopping problem and the corresponding zero-sum game has a value. Although the result seems similar to the one obtained in the classical optimal stopping theory, the mutual singularity of probabilities and the game aspect of the problem give rise to major technical hurdles, which we circum...

Acquiring markedness constraints

This paper questions the assumption made in classic Optimality Theory (Prince & Smolensky 1993 [2004]) that markedness constraints are an innate part of Universal Grammar. Instead, we argue that constraints are acquired on the basis of the language data to which L1 learning children are exposed. This is argued both on general grounds (innateness is an assumption that should not be invoked lightly) and on the basis of empirical evidence. We investigate this issue for six general markedness constraints in French, and show that all constraints could be acquired on the basis of the ambient data. Second, we show that the order of acquisition of the marked structures matches the frequency of violations of the relevant constraints in the input quite well. This argues in favour of a phonological model in which constraints are acquired, not innate, i.e. a model in which grammatical notions such as constraints are derived from language use.

On the Robust Optimal Stopping Problem

We study a robust optimal stopping problem with respect to a set P of mutually singular probabilities. This can be interpreted as a zero-sum controller-stopper game in which the stopper is trying to maximize its pay-off while an adverse player wants to minimize this payoff by choosing an evaluation criteria from P. We show that the upper Snell envelope Z of the reward process Y is a supermartingale with respect to an appropriately defined nonlinear expectation E, and Z is further an E-martingale up to the first time tau when Z meets Y . Consequently, tau is the optimal stopping time for the robust optimal stopping problem and the corresponding zero-sum game has a value. Although the result seems similar to the one obtained in the classical optimal stopping theory, the mutual singularity of probabilities and the game aspect of the problem give rise to major technical hurdles, which we circumvent using some new methods.