. Computational chemistry grew in a new era of “desktop modeling,” which coincided with a growing demand for modeling software, especially from the pharmaceutical industry. Parameterization of models in computational chemistry is an arduous enterprise, and we argue that this activity leads, in this specific context, to tensions among scientists regarding the epistemic opacity transparency of parameterized methods and the software implementing them. We relate one flame war from the Computational Chemistry mailing List in order to assess in detail (...) the relationships between modeling methods, parameterization, software and the various forms of their enclosure or disclosure. Our claim is that parameterization issues are an important and often neglected source of epistemic opacity and that this opacity is entangled in methods and software alike. Models and software must be addressed together to understand the epistemological tensions at stake. (shrink)

We study the parameterized complexity of the problem to decide whether a given natural number n satisfies a given $\Delta _0$ -formula $\varphi (x)$ ; the parameter is the size of $\varphi $. This parameterization focusses attention on instances where n is large compared to the size of $\varphi $. We show unconditionally that this problem does not belong to the parameterized analogue of $\mathsf {AC}^0$. From this we derive that certain natural upper bounds on the complexity of our (...) parameterized problem imply certain separations of classical complexity classes. This connection is obtained via an analysis of a parameterized halting problem. Some of these upper bounds follow assuming that $I\Delta _0$ proves the MRDP theorem in a certain weak sense. (shrink)

We have parameterized Einstein’s thought experiment with atomic clocks, supposing that we knew neither if the space and time are relative or absolute, nor if the speed of light was ultimate speed or not. We have obtained a Parameterized Special Theory of Relativity (PSTR) (1982). Our PSTR generalized not only Einstein’s Special Theory of Relativity, but also our Absolute Theory of Relativity, and introduced three more possible Relativities to be studied in the future. After the 2011 CERN’s superluminal neutrino experiments, (...) we recall our ideas and invite researchers to deepen the study of PSTR, ATR, and check the three new mathematically emerged Relativities 4.3, 4.4, and 4.5. (shrink)

We consider several kinds of partition relations on the set ${\mathbb{R}}$ of real numbers and its powers, as well as their parameterizations with the set ${[\mathbb{N}]^{\mathbb{N}}}$ of all infinite sets of natural numbers, and show that they hold in some models of set theory. The proofs use generic absoluteness, that is, absoluteness under the required forcing extensions. We show that Solovay models are absolute under those forcing extensions, which yields, for instance, that in these models for every well ordered partition (...) of ${\mathbb{R}^\mathbb{N}}$ there is a sequence of perfect sets whose product lies in one piece of the partition. Moreover, for every finite partition of ${[\mathbb{N}]^{\mathbb{N}} \times \mathbb{R}^{\mathbb{N}}}$ there is ${X \in [\mathbb{N}]^{\mathbb{N}}}$ and a sequence ${\{P_{k} : k \in \mathbb{N}\}}$ of perfect sets such that the product ${[X]^{\mathbb{N}} \times \prod_{k}^{\infty}P_{k}}$ lies in one piece of the partition, where ${[X]^{\mathbb{N}}}$ is the set of all infinite subsets of X. The proofs yield the same results for Borel partitions in ZFC, and for more complex partitions in any model satisfying a certain degree of generic absoluteness. (shrink)

Many parameterized problems ask, given an instance and a natural number k as parameter, whether there is a solution of size k. We analyze the relationship between the complexity of such a problem and the corresponding maximality problem asking for a solution of size k maximal with respect to set inclusion. As our results show, many maximality problems increase the parameterized complexity, while “in terms of the W-hierarchy” minimality problems do not increase the complexity. We also address the corresponding construction, (...) listing, and counting problems. (shrink)

Theory of mind refers to the human capacity for reasoning about others’ mental states based on observations of their actions and unfolding events. This type of reasoning is notorious in the cognitive science literature for its presumed computational intractability. A possible reason could be that it may involve higher-order thinking. To investigate this we formalize theory of mind reasoning as updating of beliefs about beliefs using dynamic epistemic logic, as this formalism allows to parameterize ‘order of thinking.’ We prove that (...) theory of mind reasoning, so formalized, indeed is intractable. Using parameterized complexity we prove, however, that the ‘order parameter’ is not a source of intractability. We furthermore consider a set of alternative parameters and investigate which of them are sources of intractability. We discuss the implications of these results for the understanding of theory of mind. (shrink)

Parameterized complexity has, so far, been largely confined to consideration of computational problems as decision or search problems. However, it is becoming evident that the parameterized point of view can lead to new insight into counting problems. The goal of this article is to introduce a formal framework in which one may consider parameterized counting problems.

Thomas Richardson and Peter Spirtes. Parameterizing and Scoring Mixed Ancestral Graphs.

Sparse languages play an important role in classical structural complexity theory. In this paper we introduce a natural definition of sparse problems for parameterized complexity theory. We prove an analog of Mahaney's theorem: there is no sparse parameterized problem which is hard for the tth level of the W hierarchy, unless the W hierarchy itself collapses up to level t. The main result is proved for the most general form of parametric many:1 reducibility, where the parameter functions are not assumed (...) to be recursive. This provides one of the few instances in parameterized complexity theory of a full analog of a major classical theorem. The proof involves not only the standard technique of left sets, but also substantial circuit combinatorics to deal with the problem of small weft, and a diagonalization to cope with potentially nonrecursive parameter functions. The latter techniques are potentially of interest for further explorations of parameterized complexity analogs of classical structural results. (shrink)

Mental model ascription – also called mindreading – is the process of inferring the mental states of others, which happens as a matter of course in social interactions. But although ubiquitous, mindreading is presumably a highly variable process: people mindread to different extents and with _different results._ We hypothesize that human mindreading ability relies on a large number of personal and contextual features: the inherent abilities of specific individuals, their current physical and mental states, their knowledge of the domain of (...) discourse, their familiarity with the interlocutor, the risks associated with an incorrect assessment of intent, and so on. This paper presents a theory of mindreading that models diverse artificial intelligent agents using an inventory of parameters and value sets that represent traits of humans and features of discourse contexts. Examples are drawn from Maryland Virtual Patient, a prototype system that will permit medical trainees to diagnose and treat cognitively modeled virtual patients with the optional assistance of a virtual tutor. Since real patients vary greatly with respect to physiological and cognitive features, so must a society of virtual patients. Modeling such variation is one of the goals of the overall OntoAgent program of research and development. (shrink)

We investigate the application of Courcelle’s theorem and the logspace version of Elberfeld et al. in the context of non-monotonic reasoning. Here we formalize the implication problem for propositional sets of formulas, the extension existence problem for default logic, the expansion existence problem for autoepistemic logic, the circumscriptive inference problem, as well as the abduction problem in monadic second order logic and thereby obtain fixed-parameter time and space efficient algorithms for these problems. On the other hand, we exhibit, for each (...) of the above problems, families of instances of a very simple structure that, for a wide range of different parameterizations, do not have efficient fixed-parameter algorithms (even in the sense of the large class XPnu, resp., XLnu) under standard complexity assumptions. (shrink)

We develop a dimension theory for D-semianalytic sets over an arbitrary non-Archimedean complete field. Our main results are the equivalence of several notions of dimension and a theorem on additivity of dimensions of projections and fibers in characteristic 0. We also prove a parameterized version of normalization for D-semianalytic sets.

Parameterization and parameter tuning are central aspects of climate modeling, and there is widespread consensus that these procedures involve certain subjective elements. Even if the use of these subjective elements is not necessarily epistemically problematic, there is an intuitive appeal for replacing them with more objective (automated) methods, such as machine learning. Relying on several case studies, we argue that, while machine learning techniques may help to improve climate model parameterization in several ways, they still require expert judgment (...) that involves subjective elements not so different from the ones arising in standard parameterization and tuning. The use of machine learning in parameterizations is an art as well as a science and requires careful supervision. (shrink)

A completeness theory for parameterized computational complexity has been studied in a series of recent papers, and has been shown to have many applications in diverse problem domains including familiar graph-theoretic problems, VLSI layout, games, computational biology, cryptography, and computational learning [ADF,BDHW,BFH, DEF,DF1-7,FHW,FK]. We here study the parameterized complexity of two kinds of problems: (1) problems concerning parameterized computations of Turing machines, such as determining whether a nondeterministic machine can reach an accept state in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} (...) \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $k$\end{document} steps (the Short TM Computation Problem), and (2) problems concerning derivations and factorizations, such as determining whether a word \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $x$\end{document} can be derived in a grammar \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $G$\end{document} in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $k$\end{document} steps, or whether a permutation has a factorization of length \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $k$\end{document} over a given set of generators. We show hardness and completeness for these problems for various levels of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $W$\end{document} hierarchy. In particular, we show that Short TM Computation is complete for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $W[1]$\end{document}. This gives a new and useful characterization of the most important of the apparently intractable parameterized complexity classes. (shrink)

Many natural computational problems have input consisting of two or more parts, one of which may be considered a parameter. For example, there are many problems for which the input consists of a graph and a positive integer. A number of results are presented concerning parameterized problems that can be solved in complexity classes below P, given a single word of advice for each parameter value. Different ways in which the word of advice can be employed are considered, and it (...) is shown that the class FPT of tractable parameterized problems has interesting and natural internal structure. (shrink)

The English language has adopted the word Tardis for something that looks simple from the outside but is much more complicated when inspected from the inside. The word comes from a BBC science fiction series, in which the Tardis is a machine for traveling in time and space, that looks like a phone booth from the outside. This paper claims that simulation models are a Tardis in a way that calls into question their transferability. The argument is developed taking Molecular (...) Modeling and Simulation as an example. There, simulation models are force fields that describe the molecular interactions and that look like simple and highly modular mathematical expressions. To make them work, they contain parameters that are adjusted to match certain data. The role of these parameters and the way they are obtained is seriously under-appreciated. It is constitutive for the model and central for its applicability and performance. Hence, the model is more than it seems so that working with adjustable parameters deeply affects the ontology of simulation models. This is particularly crucial for the transferability of the models: the information on how a model was trained is like luggage the model must carry on its voyage. (shrink)

This article explores the practice of simulation modeling by investigating how parameterizations are constructed and integrated into existing frameworks. Parameterizations are simplified process descriptions adapted for simulation models. On the basis of a study of meteorological research, the article presents predictive and representative construction as two different ways of developing parameterizations and the trade-offs involved in this work. Because the overall aim in predictive construction is to improve weather forecasts, the most practical solutions are chosen over the best theoretical solutions. (...) In representative construction, the situation is reversed, but while discourse focuses on theory and models, the everyday work is often tied to computer programs. These different ways of construction work are closely related to the role of the simulation models as epistemic or technical objects, and this characterization is also used to compare the results with previous research. (shrink)

Intractability is a growing concern across the cognitive sciences: while many models of cognition can describe and predict human behavior in the lab, it remains unclear how these models can scale to situations of real-world complexity. Cognition and Intractability is the first book to provide an accessible introduction to computational complexity analysis and its application to questions of intractability in cognitive science. Covering both classical and parameterized complexity analysis, it introduces the mathematical concepts and proof techniques that can be used (...) to test one's intuition of tractability. It also describes how these tools can be applied to cognitive modeling to deal with intractability, and its ramifications, in a systematic way. Aimed at students and researchers in philosophy, cognitive neuroscience, psychology, artificial intelligence, and linguistics who want to build a firm understanding of intractability and its implications in their modeling work, it is an ideal resource for teaching or self-study. (shrink)

We have two main objections to Kerr and Godfrey-Smith's (2002) meticulous analysis. First, they misunderstand the position we took in Unto Others – we do not claim that individual-level statements about the evolution of altruism are always unexplanatory and always fail to capture causal relationships. Second, Kerr and Godfrey-Smith characterize the individual and the multi-level perspectives in terms of different sets of parameters. In particular, they do not allow the multi-level perspective to use the individual fitness parameters i and i. (...) We don't see why the multi-level perspective prevents one from thinking in these terms. Kerr and Godfrey-Smith's argument that Uyenoyama and Feldman's (1980, 1992) definition of altruism belongs more to the individualist perspective than it does to the multi-level perspective is an artifact of their choice of parameters; the same point applies to their argument about the individualism inherent in the idea of Class I and Class II fitness structures. (shrink)

We prove, by explicit construction, that not all sets definable in polynomially bounded o-minimal structures have mild parameterization. Our methods do not depend on the bounds particular to the definition of mildness and therefore our construction is also valid for a generalized form of parameterization, which we call G-mild. Moreover, we present a cell decomposition result for certain o-minimal structures which may be of independent interest. This allows us to show how our construction can produce polynomially bounded, model (...) complete expansions of the real ordered field which, in addition to lacking G-mild parameterization, nonetheless still have analytic cell decomposition. (shrink)

Under the normal assumptions of quantum field theory, Haag’s theorem states that any field unitarily equivalent to a free field must itself be a free field. Unfortunately, the derivation of the Dyson series perturbation expansion relies on the use of the interaction picture, in which the interacting field is unitarily equivalent to the free field but must still account for interactions. Thus, the traditional perturbative derivation of the scattering matrix in quantum field theory is mathematically ill defined. Nevertheless, perturbative quantum (...) field theory is currently the only practical approach for addressing scattering for realistic interactions, and it has been spectacularly successful in making empirical predictions. This paper explains this success by showing that Haag’s Theorem can be avoided when quantum field theory is formulated using an invariant, fifth path parameter in addition to the usual four position parameters, such that the Dyson perturbation expansion for the scattering matrix can still be reproduced. As a result, the parameterized formalism provides a consistent foundation for the interpretation of quantum field theory as used in practice and, perhaps, for better dealing with other mathematical issues. (shrink)

Given someone’s fully specified posterior probability distribution q and information about the revision method that they employed to produce q, what can you infer about their prior probabilistic commitments? This question provides an entrée into a thoroughgoing discussion of a class of parameterizations of Jeffrey conditioning in which the parameters furnish information above and beyond that incorporated in \. Our analysis highlights the ubiquity of Bayes factors in the study of probability revision.

Relatively congruence regular quasivarieties and quasivarieties of logic have noticeable similarities. The paper provides a unifying framework for them which extends the Blok-Pigozzi theory of elementarily algebraizable (and protoalgebraic) deductive systems. In this extension there are two parameters: a set of terms and a variable. When the former is empty or consists of theorems, the Blok-Pigozzi theory is recovered, and the variable is redundant. On the other hand, a class of membership logics is obtained when the variable is the only (...) element of the set of terms. For these systems the appropriate variant of equivalent algebraic semantics encompasses the relatively congruence regular quasivarieties. (shrink)

In explaining the reasons for sustained existence of tolerance in Indian philosophical mind and continuation of tolerant practices in socio-political life, Amartya Sen argues that tolerance is inherently a social enterprise, which may appear as contingent, but for all intents and purposes is persistent. Basing his thesis that is opposed to Cartesian dualism, which makes a distinction between mind and body, Sen submits that Indian system of universalizing perception finds a subtle form of connection between mind and body. He expands (...) the ancient core worldview, Vasundhara kutumbakam as a secular tolerant civil code,1which makes a connection between the transcendental and the pragmatic planes of consciousness, and reconstructs a thesis about tolerance around human consciousness, which is collectivized and anchored in an acknowledged public space in society that is joined together psychologically as well as philosophically. Tolerance as consciousness can be regarded a necessary condition for playing the role of intentionality as stipulated by classical philosophy. Aware of this ancient wisdom that accepts relativism as an impasse over some evaluative matter, Sen avoids the pitfalls of cultural relativism in tolerance by offering an argument that is based on the metaphysics of Advaita Vedanta and other religious and secular literature, and epitomizes an internationalizing virtue in tolerant traditions. I would examine some interconnected issues, such as the ethical “perimeter” of Sen’s philosophical observation of totalized value system and Indian tolerant attitudes in real life, etc., raising the broader question about the location of cultural identity in relation to supranational state organization. My chief argument is that Sen has been able to observe a connection between the Advaita Vedantic moral philosophy that informs that viewed from the Brahmanic perspective of absolute knowledge in unity, the apparent subject of duality is not the ultimate subject. My conclusion is that valuing of tolerance, individual liberty as well as civil rights is a particular contribution of Western thinking and philosophy; the Western advocates of these rights often provide ammunition to the non-Western critics of tolerance and human rights. (shrink)

In 1979, H. Lewis shows that the computational complexity of the Boolean satisfiability problem dichotomizes, depending on the Boolean operations available to formulate instances: intractable (NP-complete) if negation of implication is definable, and tractable (in P) otherwise [21]. Recently, an investigation in the same spirit has been extended to nonclassical propositional logics, modal logics in particular [2, 3]. In this note, we pursue this line in the realm of many-valued propositional logics, and obtain complexity classifications for the parameterized satisfiability problem (...) of two pertinent samples, Kleene and Gödel logics. (shrink)

We use a result due to Rolin, Speissegger, and Wilkie to show that definable sets in certain o-minimal structures admit definable parameterizations by mild maps. We then use this parameterization to prove a result on the density of rational points on curves defined by restricted Pfaffian functions.

We investigate the index sets associated with the degree structures of computable sets under the parameterized reducibilities introduced by the authors. We solve a question of Peter Cholakand the first author by proving the fundamental index sets associated with a computable set A, {e : W e ≤ q u A} for q∈ {m, T} are Σ4 0 complete. We also show hat FPT(≤ q n ), that is {e : W e computable and ≡ q n ?}, is Σ4 (...) 0 complete. We also look at computable presentability of these classes. (shrink)

Suppose that several individuals who have separately assessed prior probability distributions over a set of possible states of the world wish to pool their individual distributions into a single group distribution, while taking into account jointly perceived new evidence. They have the option of first updating their individual priors and then pooling the resulting posteriors or first pooling their priors and then updating the resulting group prior. If the pooling method that they employ is such that they arrive at the (...) same final distribution in both cases, the method is said to be externally Bayesian, a property first studied by Madansky . We show that a pooling method for discrete distributions is externally Bayesian if and only if it commutes with Jeffrey conditioning, parameterized in terms of certain ratios of new to old odds, as in Wagner , rather than in terms of the posterior probabilities of members of the disjoint family of events on which such conditioning originates. (shrink)

Psychologists and philosophers have recently been exploring whether the mechanisms which underlie the acquisition of ‘theory of mind’ (ToM) are best charac- terized as cognitive modules or as developing theories. In this paper, we attempt to clarify what a modular account of ToM entails, and why it is an attractive type of explanation. Intuitions and arguments in this debate often turn on the role of develop- ment: traditional research on ToM focuses on various developmental sequences, whereas cognitive modules are thought (...) to be static and ‘anti-developmental’. We suggest that this mistaken view relies on an overly limited notion of modularity, and we explore how ToM might be grounded in a cognitive module and yet still afford development. Modules must ‘come on-line’, and even fully developed modules may still develop internally, based on their constrained input. We make these points con- crete by focusing on a recent proposal to capture the development of ToM in a module via parameterization. (shrink)

There is substantial support for the general idea that a formalization of comprehenders' expectations about the likely next word in a sentence helps explaining data related to online sentence processing. While much research has focused on syntactic, semantic, and discourse expectations, the present event‐related potentials (ERPs) study investigates neurolinguistic correlates of pragmatic expectations, which arise when comprehenders expect a sentence to conform to Gricean Maxims of Conversation. For predicting brain responses associated with pragmatic processing, we introduce a formal model of (...) such Gricean pragmatic expectations, using an idealized incremental interpreter. We examine whether pragmatic expectancies derived from this model modulate the amplitude of the N400, a component that has been associated with predictive processing. As part of its parameterization, the model distinguishes genuine pragmatic interpreters, who expect maximally informative true utterances, from literal interpreters, who only expect truthfulness. We explore the model's non‐trivial predictions for an experimental setup which uses picture‐sentence verification with ERPs recorded at several critical positions in sentences containing the scalar implicature trigger some. We find that Gricean expectations indeed affect the N400, largely in line with the predictions of our model, but also discuss discrepancies between model predictions and observations critically. (shrink)

We show that Bell inequalities can be violated in the macroscopic world. The macroworld violation is illustrated using an example involving connected vessels of water. We show that whether the violation of inequalities occurs in the microworld or the macroworld, it is the identification of nonidentical events that plays a crucial role. Specifically, we prove that if nonidentical events are consistently differentiated, Bell-type Pitowsky inequalities are no longer violated, even for Bohm's example of two entangled spin 1/2 quantum particles. We (...) show how Bell inequalities can be violated in cognition, specifically in the relationship between abstract concepts and specific instances of these concepts. This supports the hypothesis that genuine quantum structure exists in the mind. We introduce a model where the amount of nonlocality and the degree of quantum uncertainty are parameterized, and demonstrate that increasing nonlocality increases the degree of violation, while increasing quantum uncertainty decreases the degree of violation. (shrink)

This paper describes KRL, a Knowledge Representation Language designed for use in understander systems. It outlines both the general concepts which underlie our research and the details of KRL‐0, an experimental implementation of some of these concepts. KRL is an attempt to integrate procedural knowledge with a broad base of declarative forms. These forms provide a variety of ways to express the logical structure of the knowledge, in order to give flexibility in associating procedures (for memory and reasoning) with specific (...) pieces of knowledge, and to control the relative accessibility of different facts and descriptions. The formalism for declarative knowledge is based on structured conceptual objects with associated descriptions. These objects form a network of memory units with several different sorts of linkages, each having well‐specified implications for the retrieval process. Procedures can be associated directly with the internal structure of a conceptual object. This procedurul attachment allows the steps for a particular operation to be determined by characteristics of the specific entities involved.The control structure of KRL is based on the belief that the next generation of intelligent programs will integrate data‐directed and goal‐directed processing by using multiprocessing. It provides for a priority‐ordered multiprocess agenda with explicit (user‐provided) strategies for scheduling and resource allocation. It provides procedure directories which operate along with process frameworks to allow procedural parameterization of the fundamental system processes for building, comparing, and retrieving memory structures. Future development of KRL will include integrating procedure definition with the descriptive formalism. (shrink)

A fixed-parameter is an algorithm that provides an optimal solution to a combinatorial problem. This research-level text is an application-oriented introduction to the growing and highly topical area of the development and analysis of efficient fixed-parameter algorithms for hard problems. The book is divided into three parts: a broad introduction that provides the general philosophy and motivation; followed by coverage of algorithmic methods developed over the years in fixed-parameter algorithmics forming the core of the book; and a discussion of the (...) essential from parameterized hardness theory with a focus on W [1]-hardness, which parallels NP-hardness, then stating some relations to polynomial-time approximation algorithms, and finishing up with a list of selected case studies to show the wide range of applicability of the presented methodology. Aimed at graduate and research mathematicians, programmers, algorithm designers and computer scientists, the book introduces the basic techniques and results and provides a fresh view on this highly innovative field of algorithmic research. (shrink)

The purpose of the simultaneous measurement of noncommuting quantum observables can be viewed as the joint estimation of parameters of the density operator of the quantum system. Joint estimation involves the application of a multiply parameterized operator-valued measure. An example related to the simultaneous estimation of the position and velocity of a particle is given. Conceptual difficulties attending simultaneous measurement of noncommuting observables are avoided by this formation.

Coarse-grain models are essential to understand the biological function of DNA molecules because the length and time scales of the sequence-dependent physical properties of DNA are often beyond the reach of experimental and all-atom computational methods. Simulating coarse-grain models of DNA, e.g. using Langevin dynamics, requires the parametrization of both potential and kinetic energy functions. Many studies have shown that the flexibility (i.e., potential energy) of a DNA molecule depends on its sequence. In contrast, little is known about the sequence-dependence (...) of DNA mass parameters required to model its kinetic energy. In this paper, an algebraic expression is derived for the kinetic energy as a function of linear and angular velocities of each DNA base parameterized by its mass, center of mass, and rotational inertia tensor. The parameters of this function are then approximated from a set of fine-grain molecular dynamics simulations representing all combinations of the four DNA base pairs AT, TA, GC, and CG, in different sequence contexts. Compatibility conditions associated with the assumption of each base being modeled as a rigid body were verified to be good approximations. The kinetic parameters were found to be significantly different between the four G, C, A, and T bases, and to not be dependent on the sequence context. This suggests that the effective kinetic parameters of a DNA base may depend only on the base itself, not on its neighbors. (shrink)