Classical Optimal Theory Research Articles

Kurpian glides

Abstract This article addresses the problem of vowel-generated glides in Kurpian. In general, glides come from two sources: Gliding and Glide Insertion, for instance, word-initial /#iVC/ → [jVC] and /#iC/ → [jiC], where V stands for a vowel and C for a consonant. Even though Gliding and Glide Insertion are different phonological operations, they are united by a single goal: to eliminate onsetless syllables because a glide, regardless of whether it comes from a vowel or from insertion, provides an onset to a syllable. Onset-driven effects are particularly rich in Kurpian because they involve all kinds of vowels, including /a/ but not /ɛ/, a situation that has not been noted in the past research on crosslinguistic typologies (Levi, Susannah V. 2004. The representation of underlying glides: A cross-linguistic study. Seattle, WA: University of Washington dissertation, Levi, Susannah V. 2008. Phonemic vs. derived glides. Lingua 118. 1956–1978; Rosenthall, Sam. 1994. Vowel/glide alternation in a theory of constraint interaction. Amherst, MA: University of Massachusetts dissertation; Sands, Kathy. 2004. Patternings of vocalic sequences in the world’s languages. Santa Barbara, CA: University of California, Santa Barbra dissertation). Further, glides are found both word-medially and word-initially. In this regard, Kurpian is different from Standard Polish, which tolerates both hiatus and word-initial onsetless syllables. It is argued that the constraint interaction required cannot be accounted for in classic Optimality Theory (OT). The solution is to adopt Derivational OT.

Equivalent damping ratio oriented investigation on tuned negative stiffness inerter damper for seismic application

Additional equivalent damping ratio (EDR) plays a crucial role in the performance evaluation and design methodology of conventional passive dampers. The inclusion of inerter elements has been extensively demonstrated to significantly enhance the control efficiency of these passive dampers. Recently, negative stiffness (NS) elements have been found potential to enhance the control performance of inerter-based dampers (IBDs). However, little research has investigated the enhancement effect of NS elements on the additional EDR of IBDs. Meanwhile, the existing design methodology for IBDs is response-based, posing challenges in ensuring optimal control efficiency and fully utilizing the essential features of inerter and NS elements. In this study, the tuned negative stiffness inerter damper (TNSID), which integrates the NS element into one of the classical IBDs, namely the tuned inerter damper (TID), is investigated in terms of EDR for seismic application. This study makes two primary contributions. Firstly, it proposes an optimization design methodology aimed at achieving optimal control performance and efficiency of the TNSID simultaneously. Secondly, it unveils the enhancement law for the control performance and efficiency of TNSID. To do this, the analytical formulas for additional EDR and EDR enhancement (EDRE) factors are established as indicators of control performance and efficiency, respectively. Closed-form expressions are derived to optimize the TNSID design parameters. The comparative studies are conducted on both single and multi-degree-of-freedom primary structures, utilizing closed-form expressions, frequency transfer functions, and time history analysis. Results demonstrate that the incorporation of the NS element and the proposed optimization design methodology can further enhance both the control performance and efficiency of TNSID, surpassing those achieved by TID and classical fixed-point optimization theory.

Opacity in classic and derivational optimality theory: Tiberian Hebrew Spirantization and Polisho-Raising

Classic Optimality Theory treats phonological computation as a one-step parallel evaluation of output candidates. Such an approach does not handle well phonological opacity, in which the context of phonological processes is obscured on the surface. This article shows two examples of phonological opacity: Tiberian Hebrew Spirantization and Polish o-Raising. While these mappings are impossible to account for in classic OT, they are readily analyzed using the framework of Derivational OT.

Fifty years of mathematical growth theory: Classical topics and new trends

We present an overview of selected contributions of the Journal of Mathematical Economics’ authors to growth theory in the last half century. We start with the classical optimal growth theory within a benchmark multisector model and outline the successive developments in the analysis of this model, including the turnpike theory. Different refinements of the benchmark are considered along the way. We then survey the abundant literature on endogenous fluctuations in two-sector models. We conclude with two strong trends in the recent growth literature: green growth and infinite-dimensional growth models.

Methodology for regional industrial complex management: Architecture of an agent-based model

Industry is the backbone of the economy of developed countries and individual regions. To optimize management processes in such a complex and multi-level sector, specific economic-mathematical models and practical tools have to be developed. The paper discusses the optimal architecture of the regional industrial complex management model on a modern theoretical-methodological and instrumental (program) basis. The classical management theory, optimization theory and game theory constitute the methodology of this study. Among the research methods applied are agent-based and minimax approaches. We substantiate the use of agent-based modelling to simulate administering the regional industrial complex. The paper presents a three-tiered management architecture consisting of federal, regional and company level authorities (united by type of activity). For each level, control agents are identified and a set of indicators formed, which cover the structure of the phase vector, including its attributes, key parameters, control actions used, risks, a model of the parameters’ dynamics, and a model of the data possessed by the object. We build a hierarchical structure of administration and information relationships in the model and, based on the minimax approach, create an algorithm of agents’ efforts to select optimal control actions. The proposed architecture will allow forming a flexible toolkit for assessing industrial development scenarios and producing the best step-by-step management pattern of the regional industrial complex.

Faithfulness and underspecification

This work is about two ‘generation problems’ for classic Optimality Theory, chain shifts and saltations. The issues for OT posed by traditional analyses of chain shifts and saltations have led to various embellishments of the classic theory, typically in the form of novel constraint types. Reiss (2021a,b) proposes a general solution to the problem of chain shifts and saltations that relies more directly on different assumptions about representations than about constraints. Specifically, Reiss assumes that underlying representations may be underspecified, and that a map ‘counts’ as a chain shift or as a saltation so long as the surface alternants from a uniform underlying representation match the respective observed alternants. We report here on three results from our ongoing formal assessment of Reiss’s proposed solution.

Semi-Metric Portfolio Optimization: A New Algorithm Reducing Simultaneous Asset Shocks

This paper proposes a new method for financial portfolio optimization based on reducing simultaneous asset shocks across a collection of assets. This may be understood as an alternative approach to risk reduction in a portfolio based on a new mathematical quantity. First, we apply recently introduced semi-metrics between finite sets to determine the distance between time series’ structural breaks. Then, we build on the classical portfolio optimization theory of Markowitz and use this distance between asset structural breaks for our penalty function, rather than portfolio variance. Our experiments are promising: on synthetic data, we show that our proposed method does indeed diversify among time series with highly similar structural breaks and enjoys advantages over existing metrics between sets. On real data, experiments illustrate that our proposed optimization method performs well relative to nine other commonly used options, producing the second-highest returns, the lowest volatility, and second-lowest drawdown. The main implication for this method in portfolio management is reducing simultaneous asset shocks and potentially sharp associated drawdowns during periods of highly similar structural breaks, such as a market crisis. Our method adds to a considerable literature of portfolio optimization techniques in econometrics and could complement these via portfolio averaging.

Exact Optimal Stopping for Multidimensional Linear Switching Diffusions

The paper studies a class of multidimensional optimal stopping problems with infinite horizon for linear switching diffusions. There are two main novelties in the optimal problems considered: The underlying stochastic process has discontinuous paths, and the cost function is not necessarily integrable on the entire time horizon, where the latter is often a key assumption in classical optimal stopping theory for diffusions. Under relatively mild conditions, we show, for the class of multidimensional optimal stopping problems under consideration, that the first entry time of the stopping region is an optimal stopping time. Further, we prove that the corresponding optimal stopping boundaries can be represented as the unique solution to a nonlinear integral equation. We conclude with an application of our results to the problem of quickest real-time detection of a Markovian drift. Funding: P. Ernst received financial support from the Army Research Office [Grant ARO-YIP-71636-MA], the National Science Foundation [Grant DMS-1811936], and the Office of Naval Research [Grants N00014-18-1-2192 and N00014-21-1-2672].

Robust optimal designs using a model misspecification term

Much of classical optimal design theory relies on specifying a model with only a small number of parameters. In many applications, such models will give reasonable approximations. However, they will often be found not to be entirely correct when enough data are at hand. A property of classical optimal design methodology is that the amount of data does not influence the design when a fixed model is used. However, it is reasonable that a low dimensional model is satisfactory only if limited data is available. With more data available, more aspects of the underlying relationship can be assessed. We consider a simple model that is not thought to be fully correct. The model misspecification, that is, the difference between the true mean and the simple model, is explicitly modeled with a stochastic process. This gives a unified approach to handle situations with both limited and rich data. Our objective is to estimate the combined model, which is the sum of the simple model and the assumed misspecification process. In our situation, the low-dimensional model can be viewed as a fixed effect and the misspecification term as a random effect in a mixed-effects model. Our aim is to predict within this model. We describe how we minimize the prediction error using an optimal design. We compute optimal designs for the full model in different cases. The results confirm that the optimal design depends strongly on the sample size. In low-information situations, traditional optimal designs for models with a small number of parameters are sufficient, while the inclusion of the misspecification term lead to very different designs in data-rich cases.

A novel optimized grey model and its application in forecasting CO[formula omitted] emissions

Carbon dioxide emissions are the main cause of global warming. At present, how to reduce carbon dioxide emissions while promoting energy savings and emission reduction is a hot research topic. Hence, China’s carbon dioxide emissions must be reasonably and accurately predicted because it is very important for the Chinese government to formulate energy and environmental policies. In this study, the classical optimization theory of the Fibonacci sequence and golden ratio were applied to the grey prediction model of an approximately inhomogeneous exponential series. Then, a new optimization model was established, and the properties of the optimization model were studied. The purpose is to reduce the parameter estimation errors of the model and improve the simulation and prediction accuracy of the model. Next, the novel model was applied to the simulation and prediction of CO2 emissions in China. The experimental results show that the effectiveness of the novel model was much better than that of the other models, which confirms the effectiveness of the new model. Based on this, China’s carbon dioxide emissions were predicted and analysed. The results show that China’s carbon dioxide emissions will still be on the rise over the next five years, and carbon dioxide emissions remain a serious problem.

Accelerated Convergence of Contracted Quantum Eigensolvers through a Quasi-Second-Order, Locally Parameterized Optimization.

A contracted quantum eigensolver (CQE) finds a solution to the many-electron Schrödinger equation by solving its integration (or contraction) to the two-electron space—a contracted Schrödinger equation (CSE)—on a quantum computer. When applied to the anti-Hermitian part of the CSE (ACSE), the CQE iterations optimize the wave function, with respect to a general product ansatz of two-body exponential unitary transformations that can exactly solve the Schrödinger equation. In this work, we accelerate the convergence of the CQE and its wave function ansatz via tools from classical optimization theory. By treating the CQE algorithm as an optimization in a local parameter space, we can apply quasi-second-order optimization techniques, such as quasi-Newton approaches or nonlinear conjugate gradient approaches. Practically, these algorithms result in superlinear convergence of the wave function to a solution of the ACSE. Convergence acceleration is important because it can both minimize the accumulation of noise on near-term intermediate-scale quantum (NISQ) computers and achieve highly accurate solutions on future fault-tolerant quantum devices. We demonstrate the algorithm, as well as some heuristic implementations relevant for cost-reduction considerations, comparisons with other common methods such as variational quantum eigensolvers, and a Fermionic-encoding-free form of the CQE.

Dark Type Dynamical Systems: The Integrability Algorithm and Applications

Based on a devised gradient-holonomic integrability testing algorithm, we analyze a class of dark type nonlinear dynamical systems on spatially one-dimensional functional manifolds possessing hidden symmetry properties and allowing their linearization on the associated cotangent spaces. We described main spectral properties of nonlinear Lax type integrable dynamical systems on periodic functional manifolds particular within the classical Floquet theory, as well as we presented the determining functional relationships between the conserved quantities and related geometric Poisson and recursion structures on functional manifolds. For evolution flows on functional manifolds, parametrically depending on additional functional variables, naturally related with the classical Bellman-Pontriagin optimal control problem theory, we studied a wide class of nonlinear dynamical systems of dark type on spatially one-dimensional functional manifolds, which are both of diffusion and dispersion classes and can have interesting applications in modern physics, optics, mechanics, hydrodynamics and biology sciences. We prove that all of these dynamical systems possess rich hidden symmetry properties, are Lax type linearizable and possess finite or infinite hierarchies of suitably ordered conserved quantities.

Recent Advances in Robust Design for Accelerated Failure Time Models with Type I Censoring

Many fields including clinical and manufacturing areas usually perform life-testing experiments and accelerated failure time models (AFT) play an essential role in these investigations. In these models the covariate causes an accelerant effect on the course of the event through the term named acceleration factor (AF). Despite the influence of this factor on the model, recent studies state that the form of AF is weakly or partially known in most real applications. In these cases, the classical optimal design theory may produce low efficient designs since they are highly model dependent. This work explores planning and techniques that can provide the best robust designs for AFT models with type I censoring when the form of the AF is misspecified, which is an issue little explored in the literature. Main idea is focused on considering the AF to vary over a neighbourhood of perturbation functions and assuming the mean square error matrix as the basis for measuring the design quality. A key result of this research was obtaining the asymptotic MSE matrix for type I censoring under the assumption of known variance regardless the selected failure time distribution. In order to illustrate the applicability of previous result to a study case, analytical characterizations and numerical approaches were developed to construct optimal robust designs under different contaminating scenarios for a failure time following a log-logistic distribution.

A new multi-level algorithm for balanced partition problem on large scale directed graphs

Graph partition is a classical combinatorial optimization and graph theory problem, and it has a lot of applications, such as scientific computing, VLSI design and clustering etc. In this paper, we study the partition problem on large scale directed graphs under a new objective function, a new instance of graph partition problem. We firstly propose the modeling of this problem, then design an algorithm based on multi-level strategy and recursive partition method, and finally do a lot of simulation experiments. The experimental results verify the stability of our algorithm and show that our algorithm has the same good performance as METIS. In addition, our algorithm is better than METIS on unbalanced ratio.

Italian preconsonantal s-voicing is not regressive voice assimilation

AbstractIn the literature of laryngeal phonology Romance languages are considered voice languages, exhibiting a binary distinction between a voiced lenis and a voiceless fortis set of obstruents. Voice languages are characterised by regressive voice assimilation (RVA) due to the phonological activity of [voice]. Italian manifests a process similar to RVA, called preconsonantal s-voicing; that is, /s/ becomes voiced before voiced consonants. Since /sC/ is the only obstruent cluster in Italian phonotactics, Italian seems to fulfil the requirements for being a prototypical voice language. However, this paper argues that s-voicing is not an instance of RVA, at least from a synchronic phonological point of view. RVA and Italian preconsonantal s-voicing essentially differ at every level of a synchronic comparison: in the input, in the trigger, in the domain of application and in the frequency of the processes. In Italian only sibilant fricatives may undergo voicing before consonants; however, other obstruents (which mostly appear in loanwords) do not assimilate for [voice]. Italian preconsonantal s-voicing does not take place at the word boundary or at morpheme boundaries, and it seems to be optional is new loanwords; thus, it is not a postlexical process like RVA. The synchronic differences between the two phenomena are analysed in Classical Optimality Theory. The laryngeal system of Italian prefers faithfulness over markedness, which means that non-/sC/ obstruent clusters surface with underlying voice values; while the voicing of /s/ before voiced consonants is seen as phonetic and not phonological.

Shotgun Weddings in Control Engineering and Postwar Economics, 1940–72

During World War II there was a “shotgun wedding” forged in the processes of designing feedback mechanisms used to control gunfire targeting fast-moving enemy aircraft. Hendrik Bode perceived the shotgun marriage as a union of the classic regulator approach and long-distance telephone communications engineering. Norbert Weiner took the wedding description a step further by nesting communication engineering into a statistical mechanics framework in which the information engineer had to filter the useful signal from the useless noise. A main goal in designing weapon-fire control systems was to use negative feedback loops to ensure the stability of a system that was always in a transient mode. In the 1950s, control engineers such as Arnold Tustin, Bill Phillips, and Charles Holt offered their new analytic tools of block diagrams of systems with feedback loops, stability criteria, and physical analogues to model the economy, realize the promise of stability of employment and prices, and avoid another depression similar to that of the 1930s. By the early 1970s Paul Samuelson and the rational expectations theorists were primed to be receptive to a second, Cold War shotgun wedding in control engineering. Richard Bellman described it as a marriage of classical optimization theory and the probabilistic theory of stochastic processes.

Optimization for Deep Learning: An Overview

Optimization is a critical component in deep learning. We think optimization for neural networks is an interesting topic for theoretical research due to various reasons. First, its tractability despite non-convexity is an intriguing question and may greatly expand our understanding of tractable problems. Second, classical optimization theory is far from enough to explain many phenomena. Therefore, we would like to understand the challenges and opportunities from a theoretical perspective and review the existing research in this field. First, we discuss the issue of gradient explosion/vanishing and the more general issue of undesirable spectrum and then discuss practical solutions including careful initialization, normalization methods and skip connections. Second, we review generic optimization methods used in training neural networks, such as stochastic gradient descent and adaptive gradient methods, and existing theoretical results. Third, we review existing research on the global issues of neural network training, including results on global landscape, mode connectivity, lottery ticket hypothesis and neural tangent kernel.

Foundation of quantum optimal transport and applications

Quantum optimal transportation seeks an operator which minimizes the total cost of transporting a quantum state to another state, under some constraints that should be satisfied during transportation. We formulate this issue by extending the Monge–Kantorovich problem, which is a classical optimal transportation theory, and present some applications. As an example, we address infinitely repeated quantum games and establish the folk theorem of the quantum prisoners’ dilemma, which claims mutual cooperation can be an equilibrium of the infinitely repeated quantum game. We also exhibit a series of examples which show generic and practical advantages of the abstract quantum optimal transportation theory.

The Determination of Concession Period for Build-Operate-Transfer Solar Photovoltaic Power Project under Policy Incentives: A Case Study of China

Since the concession period is one of the most crucial variables influencing the success of a photovoltaic (PV) power project under build-operate-transfer (BOT) mode, this paper presents a real option game model—which integrates the real option and cooperative game theory—to determine the optimal concession period of the BOT solar PV power project under policy incentives by considering the value of the option to defer. In the proposed model, an effective interval of concession period for the BOT project was identified by using a real option, and the equilibrium value of the concession period was obtained by applying classical optimization theory. To evaluate our model, we empirically determined the optimal concession period for the BOT solar PV power project in China, and a sensitivity analysis was conducted to demonstrate how relevant influential factors, which are presented in the model, affect the equilibrium value of the concession period and its effective interval. The results indicate that the current investment environment in China could successfully implement the BOT solar PV power project under policy incentives, including initial cost subsidy and the feed-in tariffs mechanism. While the high volatility of electricity demand, investment cost, and land-use rent fee can lead the failure of the BOT solar PV project implementation, promoting the technological development of PV power generation, maintaining the market stability, and increasing the policy incentives can help the BOT power project to be arranged with an optimal concession period. In addition, the feed-in tariffs mechanism is more helpful than the initial cost subsidy for winning the BOT contract.

Estimating matching affinity matrices under low-rank constraints

AbstractIn 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 that effectively enforces a rank constraint on the affinity matrix. The low-rank matrix estimated in this way reveals the main factors that are relevant for matching.