Dissertations / Theses on the topic 'Equivalence'
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Asghari, Amir Hossein. "Equivalence." Thesis, University of Warwick, 2005. http://wrap.warwick.ac.uk/62104/.
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This thesis seeks to answer one single question: "what is an equivalence relation?" A more correct, though longer, version of this question is "what are the qualitatively different ways in which people experience an equivalence relation?" The second question is not simply a version of the first one. It has a completely different nature and consequently demands a completely different answer. The answer to the first question can be found in any textbook on the foundations of mathematics; while the second question can be answered only by conducting research where people are given a chance to reveal their conceptions of equivalence relations. These two questions embody two integrated phases of this thesis linked together with a transitory phase. The first phase starts with a definite answer to the first question, i.e. the standard definition of equivalence relations. This definition is used to design a certain situation consisting of certain tasks embodying the corresponding notion. The initial intention of the situation is to get students to define certain predetermined concepts related to the notion of interest, and the effectiveness of the situation is characterized by the extent of students' success to do so. The tasks are tried out on a smallish sample of students. To put it bluntly, the situation fails to achieve its aim. In the process of interviewing the students it becomes clear that the standard definition is just an advanced means of organizing by which the given situation {and many others} can be organized. More importantly, there is a growing realization that the initial intention of the study ignores the richness of the students' ways of organizing the situation in favour of maintaining a narrow criterion for success. Relinquishing the latter in favour of the former is the turning point from the first phase to the second. The second phase is a transitory phase in which more weight has been put on what students use to organize the given situation. Although the focus of this phase is not on the notion of equivalence relation, the students' works reveal some unexpected aspects of this notion. This suggests the possibility of using the original tasks for pursuing an unexpected purpose in the main (i.e. third) phase of this thesis. The main phase of the thesis adopts a phenomenographic approach to reveal students' conceptions of equivalence relations. These conceptions are inferred from the ways that the students tackle the tasks, regardless of the extent to which they fit into the standard account. It is shown that these conceptions correspond to certain 'historical' counterparts, where some prominent mathematicians of the past have tackled certain situations that from the vantage point of today's mathematics embody the idea of equivalence relation. These correspondences put forward a critical distinction between "equivalence" as an experience and "equivalence" as a concept. This distinction calls into question the most popular view of the subject: that the mathematical notion of equivalence relation is the result of spelling out our experience of equivalence. Moreover, the findings of this study suggest that the standard definition of an equivalence relation is ill-chosen from a pedagogical point of view, but well-crafted from a mathematical point of view.
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Liberato, Alessandro. "A Study on Bisimulation Equivalence and Team Equivalence." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/19128/.
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Nella prima parte della tesi viene studiata l'equivalenza per bisimulazione per comportamenti regolari, e vengono confrontati due meccanismi di ricorsione che sono stati proposti in letteratura, in particolare due istanze specifiche: finite-state CCS ed SFM. Questo confronto ha come obbiettivo quello
di capire i pro e i contro dei due approcci.
Nella seconda parte della tesi viene approfondita un'altra relazione di equivalenza basata sulla bisimulazione, ovvero la team equivalenza, per una classe di reti di Petri chiamate finite-state machine.
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Klymchuk, Tetiana. "Stratification theory of matrix pairs under equivalence and contragredient equivalence." Doctoral thesis, Universitat Politècnica de Catalunya, 2019. http://hdl.handle.net/10803/667132.
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We develop the theory of perturbations of matrix pencils basing on their miniversal deformations. Several applications of this theory are given.
All possible Kronecker pencils that are canonical forms of pencils in an arbitrary small neighbourhood of a given pencil were described by A. Pokrzywa (Linear Algebra Appl., 1986). His proof is very abstract and unconstructive. Even more abstract proof of Pokrzywa’s theorem was given by K. Bongartz (Advances in Mathematics, 1996); he uses the representation theory of finite dimensional algebras.
The main purpose of this thesis is to give a direct, constructive, and rather elementary proof of Pokrzywa’s theorem. We first show that it is sufficient to prove Pokrzywa’s theorem only for pencils that are direct sums of at most two indecomposable Kronecker pencils. Then we prove Pokrzywa’s theorem for such pencils. The latter problem is very simplified due to the following observation: it is sufficient to find Kronecker's canonical forms of only those pencils that are obtained by miniversal perturbations of a given pencil. We use miniversal deformations of matrix pencils that are given by M. I. García-Planas and V. V. Sergeichuk (Linear Algebra Appl., 1999) because their deformations have many zero entries unlike the miniversal deformations given by A. Edelman, E. Elmroth, and B. Kagstrom (SIAM J. Matrix Anal. Appl., 1997). Thus, we give not only all possible Kronecker’s canonical forms, but also the corresponding deformations of a given pencil, which is important for applications of this theory.
P. Van Dooren (Linear Algebra Appl., 1979) constructed an algorithm for computing all singular summands of Kronecker’s canonical form of a matrix pencil. His algorithm uses only unitary transformations, which improves its numerical stability. We extend Van Dooren’s algorithm both to square complex matrices under consimilarity transformations and to pairs of complex matrices under mixed equivalence.
We describe all pairs (A, B) of m-by-n and n-by-m complex matrices for which the product CD is a versal deformation of AB, in which (C, D) is the miniversal deformation of (A, B) under contragredient equivalence given by M. I. García-Planas and V. V. Sergeichuk (Linear Algebra Appl., 1999).
We find all canonical matrix pairs (A, B) under contragredient equivalence, for which the first order induced perturbations are nonzero for all nonzero miniversal deformations of (A, B). This problem arises in the theory of differential matrix equations dx= ABx.
A complex matrix pencil is called structurally stable if there exists its neighbourhood in which all pencils are strictly equivalent to it. We describe all complex matrix pencils that are structurally stable. We show that there are no pairs of complex matrices that are structurally stable with respect to contragredient equivalence.Es desenvolupa la teoria de pertorbacions de feixos de matrius a partir de les seves deformacions miniversals. Es donen diverses aplicacions d'aquesta teoria. A. Pokrzywa (Linear Algebra Appl., 1986) va descriure tots els possibles feixos en la seva forma de Kronecker que són formes canòniques dels feixos que es poden trobar en un petit entorn arbitrari d'un feix prèviament determinat. La demostració que presentava és molt abstracta i no constructiva. K. Bongartz (Advances in Mathematics, 1996) va donar una demostració encara més abstracta del teorema de Pokrzywa; utilitzant resultats de la teoria de representació d'àlgebres de dimensió finita. L’objectiu principal de aquesta tesi és presentar una demostració directa, constructiva i bastant elemental del teorema de Pokrzywa. Primer, es demostra que per a provar el teorema de Pokrzywa és suficient provar-lo solament per a feixos que són sumes directes de, com màxim, dos feixos de Kronecker indescomponibles. Per a continuació, provar el teorema de Pokrzywa per aquests feixos. L’últim problema es simplifica molt degut a la següent observació: és suficient per trobar les formes canòniques de Kronecker de només aquells feixox que s’obtenen de deformacions miniversals d’un feix determinat. Utilitzem les deformacions de feixos de matrius obtingudes per MI García-Planas i VV Sergeichuk (Linear Algebra Appl., 1999) perquè les seves deformacions tenen moltes entrades nul·les, a diferència de les deformacions miniversals obtingudes per A. Edelman, E. Elmroth i B. Kagstrom (SIAM J. Matrix Anal. Appl., 1997). Per tant, no solament donem totes les formes canòniques de Kronecker possibles, sinó també les deformacions corresponents a un feix prèviament fixat, la qual cosa és important per a les aplicacions d’aquesta teoria. P. Van Dooren (Linear Algebra Appl., 1979) va construir un algoritme per calcular tots els sumands singulars de la forma canònica de Kronecker, d’un feix de matrius. El seu algoritme utilitza solament transformacions unitàries, el que millora la seva estabilitat numèrica. Estenem l’algoritme de Van Dooren tant a matrius complexes quadrades respecte transformacions de cosimilaritat com a parells de matrius complexes respecte l’equivalència mixta. Descrivim tots els parells (A, B) de matrius complexes m per n i n per m, per les quals el producte CD és una deformació versal de AB, en la que (C, D) és la deformació miniversal de (A, B) respecte l’equivalència contragredient donada per MI García-Planas y VV Sergeichuk (Linear Algebra Appl., 1999). Descrivim tots los pares de matrius canòniques (A, B) respecte l’equivalència contragredient, per les quals les pertorbacions de primer ordre induïdes són diferents de cero para totes les deformacions miniversals no nul·les d¿(A, B). Aquest problema apareix en la teoria de les equacions matricials diferencials dx = ABx. Un feix de matrius complexes es diu estructuralment estable si existeix un entorn en el que tots els feixos són equivalents a ell respecte una relació d’equivalència considerada. Descrivim tots els feixos de matrius complexes que són estructuralment estables respecte la equivalència estricta. Mostrem que no hi ha parelles de matrius complexes que són estructuralment estables respecto l’equivalència contragredient.
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Garcia, Anna Rosio. "Relating Relations: The Impact of Equivalence-Equivalence Training on Analogical Reasoning." Scholar Commons, 2014. https://scholarcommons.usf.edu/etd/5372.
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A well-researched line showing equivalence performances in a wide variety of areas has been conducted in the field of Behavior Analysis (BA). One area demonstrates that relating relations is a behavioral account of analogical thinking. Relating relations may have implications for the development of analogical training given that analogical reasoning is seen as the foundation of intelligence yet research in this area is limited. A protocol by Stewart, Barnes-Holmes, and Weil (2009) was developed to train children in analogical reasoning using equivalence-equivalence relations. The purpose of this study was to evaluate an equivalence-equivalence training protocol based on Stewart et al. (2009) and test whether the protocol was effective in training equivalence-equivalence responding to 7 and 8-year-old children. A secondary purpose was to test whether training in equivalence-equivalence responding increased performances on analogical tests. All five participants were dismissed throughout the study. Participant 1 was dismissed during the pre-assessments and all other participants were dismissed during intervention. Because none of the participants passed the equivalence-equivalence training, increases in performance in analogical testes were not analyzed. Individual performance data from training are examined and analyzed to provide an account of the failures to pass the equivalence-equivalence protocol.
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Henderson, Troy Lee IV. "Causal equivalence of frames." Texas A&M University, 2005. http://hdl.handle.net/1969.1/4392.
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Frames have recently become popular in the area of applied mathematics known
as digital signal processing. Frames offer a level of redundancy that bases do not
provide. In a sub-area of signal processing known as data recovery, redundancy has
become increasingly useful; therefore, so have frames. Just as orthonormal bases are
desirable for numerical computations, Parseval frames provide similar properties as
orthonormal bases while maintaining a desired level of redundancy. This dissertation
will begin with a basic background on frames and will proceed to encapsulate my
research as partial fulfillment of the requirements for the Ph.D. degree in Mathematics
at Texas A&M University. More specifically, in this dissertation we investigate an
apparently new concept we term causal equivalence of frames and techniques for
transforming frames into Parseval frames in a way that generalizes the Classical Gram-
Schmidt process for bases. Finally, we will compare and contrast these techniques.
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Adji, Artidiatun. "Essays on Ricardian Equivalence." Digital Archive @ GSU, 2007. http://digitalarchive.gsu.edu/econ_diss/19.
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The theme of this dissertation is Ricardian equivalence, and its objective is to examine the effects of government debt on private consumption expenditures (Essay One), on interest rates (Essay Two), on the current account balance (Essay Three), and on individual intertemporal decision-making (Essay Four). The effects of government debt are important if debt is neutral (e.g., if “Ricardian equivalence” holds), then a stabilization program that is based on demand management policy to curtail fiscal deficits will not be operative. On the other hand, if debt is not neutral (or if Ricardian equivalence does not hold), then deficit finance may induce private consumption, boost interest rates, crowd out investment, and retard economic growth. Essay One contributes to the existing literature by taking into account the nature of liquidity constraints in a developing economy in an aggregate consumption function. Previous empirical tests on Ricardian equivalence have not considered the role of a dominant resource aspect of a country. Essay Two and Essay Three incorporate a dominant resource aspect in Indonesia by estimating the oil-macroeconomic relationship. Furthermore, Essay Three takes into account the role of capital inflows by including debt securities. Essay Four uses experimental economics methods to examine the role of distortionary taxes on Ricardian equivalence. There have been only a few studies that use an experimental approach to examine the effect of deficit spending on consumption expenditures, but these existing experimental studies ignore the role of distortionary taxes in affecting subjects’ consumption-saving decisions and focus on the presence of liquidity constraints, myopia, and uncertainty on future income. Essay Four contributes to the Ricardian equivalence literature by taking into account distortionary taxes in a Ricardian institution by levying taxes on savings in an intertemporal individual consumption-savings decision in laboratory experiments. By utilizing the aggregate consumption function and the Euler equation consumption function, Essay One shows that Indonesian consumers tend to behave in a non-Ricardian way. Public debt most likely will lead to crowding out of investment, and will retard capital accumulation and economic growth. The extent to which individuals perceive government expenditures as complements for their consumption is substantial. An increase in government expenditures will increase the marginal utility of private consumption and has an expansionary effect on aggregate demand. The complementarity between private consumption and government expenditures may be partly due to the allocation of government subsidies to basic goods and services such as electricity, fuel, fertilizer, health centers, and education. Liquidity constraints may cause consumption to have an excess sensitivity to income. The short-run and long-run aggregate consumption function estimates show that income affects consumption, indicating that consumers follow a “rule of thumb” of consuming their current income. A high ratio of public debt to gross domestic product (GDP) in Indonesia may also be the culprit of the excess sensitivity of private consumption to income. Due to low salaries in the formal sector, employees have been engaged in moonlighting activities, mostly in the form of self-employment (e.g., opening retail stores or services). This phenomenon may help to explain why private credit−which amounts to 29 percent of GDP−fails to explain consumption behavior. Most loans are made for investment rather than for consumption. Consumers’ behavior is insensitive to taxation, which perhaps is due to the fact that tax enactment is not explicitly revealed in Indonesia (e.g., price tags in the supermarket include the sales tax, and employees are only informed about their after-tax net wage instead of their gross wage). The share of tax collections to GDP averages only about 15 percent. There is still a large portion of the population who do not pay taxes or who pay far below what they should pay. The fiscal authority needs to focus more attention on alternative financing, i.e. taxation, whose system is essential to be enhanced. Essay Two shows that by excluding oil prices, deficits and debt significantly increase the real interest rate, thereby invalidating Ricardian equivalence. The evidence shows some preference for debt and deficit over government expenditures as determinants of interest rates. Inclusion of the oil price weakens the Neoclassical results, providing more support for the Ricardian paradigm. Deficits no longer increase interest rates, yet debt still significantly increases interest rates. This result reflects a loss of momentum for the Indonesian government two decades ago to decrease its dependency on debt. The government could have used the windfall oil revenue to pay off foreign debt; instead, the windfall was spent on import-intensive infrastructure development projects, in order to build domestic industry and to subsidize rice and petroleum products. The importance of oil prices in the interest rate estimation suggests that in modeling the Indonesian macroeconomy, the oil sector should be incorporated. The non-stationary nature of the stock of debt implies the failure of intertemporal budget balance to hold, indicating that the debt-financed deficit is unsustainable. Essay Three shows that around 80 percent of the estimation results provide support for the Neoclassical view, a result that is consistent with the twin deficits hypothesis. The long-run estimates indicate an almost one-to-one relationship between the government budget and the trade balance, while the short-run estimates show a smaller magnitude. When capital inflows are included, the twin deficits phenomenon is less pronounced in the short-run and disappears in the long-run. An increase in the oil price statistically and significantly improves the trade balance in the short-run and in the long-run. Essay Four shows that subjects fully anticipate an increase in future taxation by increasing the amount bequeathed in one-to-one correspondence to the increase in debt. Even under a Ricardian institution, the distorting nature of taxes on savings alters subjects’ consumption-savings decisions. The equality of the change in bequests and the change in deficit spending is not attained under the savings taxes treatment, invalidating Ricardian equivalence. In line with the results of Essays One, Two, and Three, which suggest the vital need to enhance the taxation system, the results of Essay Four entail the importance of taxes on interest income in Indonesia.
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Sequoiah-Grayson, Sebastian. "Information and logical equivalence." Thesis, University of Oxford, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.496650.
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Randell, Thomas David William. "Stimulus equivalence and naming." Thesis, University of Southampton, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.312896.
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Afara, Bassima. "Morita equivalence of semigroups." Thesis, Heriot-Watt University, 2012. http://hdl.handle.net/10399/2637.
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Morita equivalence is a general way of classifying structures by means of their actions that is weaker than isomorphism but at the same time useful. It arose first in the study of unital rings in the 1950’s [35] but has since been extended to many other kinds of strucures, including classes of non- unital rings. It was first applied to semigroup theory in the 1970’s in the work of Banaschewski [5] and Knauer [19] who independently determined when two monoids were Morita equivalent. However they were unable to extend their definition to arbitrary semigroups since Banaschewski showed that Morita equivalence reduced to isomorphism. It was not until the 1990’s that Talwar [40, 41] was able to find a good definition of Morita equivalence for a class of semigroups that included all monoids but also all regular semigroups: the class of semigroups with local units. Such a semigroup is one in which each element has a left and a right idempotent identity. Talwar’s work was not developed further until the twenty-first century when a variety of mathematicians including Funk, Laan, Lawson, M´arki and Steinberg started to develop the Morita theory of semigroups in detail [9, 20, 25, 39]. Our thesis takes as its starting point Lawson’s reinterpretation of Talwar’s work. The thesis consists of three chapters. An essential ingredient in Morita theory is the notion of an equivalence of categories. For this reason, Chapter 1 of this thesis reviews all the categorical definitions needed. In Chapter 2, we describe in detail the work of Banaschewski and Knauer on the Morita theory of monoids. These two chapters contain no new work. We begin Chapter 3 by explaining why the obvious way of defining the Morita equivalence of two semigroups does not work. We then describe Lawson’s approach to Talwar’s work. This provides the foundation for our thesis. Our new contributions to the theory are contained in Sections 3.2, 3.3 and 3.4 and are based on Rees matrix semigroups. Talwar showed that the classical Rees matrix theorem for completely simple semigroups could be regarded as a Morita theorem: a semigroup is Morita equivalent to a group if and only if it is completely simple if and only if it is isomorphic to a Rees matrix semigroup over a group. This raises the question of determining what role Rees matrix semigroups play in the Morita theory of semigroups with local units. We investigate three different problems based on this idea: Section 3.2 In this section, we try to provean exact generalisation of the Rees theorem. We are interested in the case where S is Morita equivalent to T if and only if S is isomorphic to some kind of Rees matrix semigroup over T. Section 3.3 In this section, we prove that S is Morita equivalent to T if and only if S is a locally isomorphic image of a special kind of Rees matrix semigroup over T. This result was first proved by Laan and M´arki [20] but we give a new proof that generalizes the classical proof of the Rees theorem. Section 3.4 Finally, we solve the following problem: given an inverse semi-group S find all inverse semigroups T which are Morita equivalent to S. Our solution uses special kinds of Rees matrix semigroups over S. In this section, we also describe those semigroups which are Morita equivalent to semigroups with commuting idempotents. This builds on early work by Khan and Lawson [17, 18].
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Sou, Man Chong. "Distance to the convex hull of an equivalence class by special orthogonal equivalence." Thesis, University of Macau, 2000. http://umaclib3.umac.mo/record=b1446694.
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Guo, Xiuzhan. "Monadicity, purity and descent equivalence /." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp02/NQ59136.pdf.
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Cirovic, Branislav. "Equivalence relations of synchronous schemes." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape3/PQDD_0031/NQ62448.pdf.
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Morgan, Jane Louise. "Stimulus equivalence and developmental dyslexia." Thesis, Bangor University, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.362133.
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McVeigh, Brian. "Multiple functions in equivalence classes." Thesis, University of Ulster, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.414095.
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Netolická, Karolína. "Equivalence checking of retimed circuits." Thesis, Massachusetts Institute of Technology, 2005. http://hdl.handle.net/1721.1/32104.
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Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2005.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Includes bibliographical references (p. 25).
This thesis addresses the problem of verifying the equivalence of two circuits, one or both of which have undergone register retiming as well as logic resynthesis. The aim of the thesis is to improve the ability of Formality, an equivalence checking tool written at Synopsys, to handle retimed circuits. At the beginning of this project Formality already had an implementation of peripheral retiming, an algorithm that can handle a large set of retimed circuits. In this thesis, I explain the performance, usability and special case coverage problems found in the original implementation. I review other retiming verification algorithms and conclude that none of them would perform satisfactorily in Formality. Finally, I explain the modifications made to peripheral retiming in order to solve some of the identified issues and propose partial solutions for the problems that have not been solved yet.
by Karolína Netolická.
M.Eng.
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Jacinto, Bruno. "Necessitism, contingentism and theory equivalence." Thesis, University of St Andrews, 2016. http://hdl.handle.net/10023/8814.
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Two main questions are addressed in this dissertation, namely: 1. What is the correct higher-order modal theory; 2. What does it take for theories to be equivalent. The whole dissertation consists of an extended argument in defence of the joint truth of two higher-order modal theories, namely, Plantingan Moderate Contingentism, a higher-order necessitist theory advocated by Plantinga (1974) and committed to the contingent being of some individuals, and Williamsonian Thorough Necessitism, a higher-order necessitist theory advocated by Williamson (2013) and committed to the necessary being of every possible individual. The case for the truth of these two theories relies on defences of the following metaphysical theses: i) Thorough Serious Actualism, according to which no things could have been related and yet be nothing, ii) Higher-Order Necessitism, according to which necessarily, every higher-order entity is necessarily something. It is shown that Thorough Serious Actualism and Higher-Order Necessitism are both implicit commitments of very weak logical theories. Prima facie, Plantingan Moderate Contingentism and Williamsonian Thorough Necessitism are jointly inconsistent. The argument for their joint truth thus relies also on showing i) their equivalence, and ii) that the dispute between Plantingans and Williamsonians is merely verbal. The case for i) and ii) relies on the Synonymy Account, an account of theory equivalence developed and defended in the dissertation. According to the account, theories are equivalent just in case they have the same structure of entailments and commitments, and the occupiers of the places in that structure are the same propositions. An immediate consequence of the Synonymy Account is that proponents of synonymous theories are engaged in merely verbal disputes. The Synonymy Account is also applied to the debate between noneists and Quineans, revealing that what is in question in that debate is what are the expressive resources available to describe the world.
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Швачко, Світлана Олексіївна, Svitlana Oleksiivna Shvachko, and Светлана Алексеевна Швачко. "Congruence via equivalence (translation aspects)." Thesis, Издательство Волго-Вятской академии гос.службы, 2009. http://essuir.sumdu.edu.ua/handle/123456789/2805.
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Lavado, G. J. "DESCRIPTIONAL COMPLEXITY AND PARIKH EQUIVALENCE." Doctoral thesis, Università degli Studi di Milano, 2015. http://hdl.handle.net/2434/263438.
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The thesis deals with some topics in the theory of formal languages and automata. Specifically, the thesis deals with the theory of context-free languages and the study of their descriptional complexity.
The descriptional complexity of a formal structure (e.g., grammar, model of automata, etc) is the number of symbols needed to write down its description. While this aspect is extensively treated in regular languages, as evidenced by numerous references, in the case of context-free languages few results are known.
An important result in this area is the Parikh’s theorem. The theorem states that for each context-free language there exists a regular language with the same Parikh image. Given an alphabet Σ = {a1, . . . , am}, the Parikh image is a function ψ : Σ^∗→ N^m that associates with each word w∈Σ^∗, the vector ψ(w)=(|w|_a1, |w|_a2, . . . , |w|_am), where |w|_ai is the number of occurrences of ai in w. The Parikh image of a language L⊆Σ^∗ is the set of Parikh images of its words. For instance, the language {a^nb^n | n ≥ 0} has the same Parikh image as (ab)^∗. Roughly speaking, the theorem shows that if the order of the letters in a word is disregarded, retaining only the number of their occurrences, then context-free languages are indistinguishable from regular languages.
Due to the interesting theoretical property of the Parikh’s theorem, the goal of this thesis is to study some aspects of descriptional complexity according to Parikh equivalence. In particular, we investigate the conversion of one-way nondeterministic finite automata and context-free grammars into Parikh equivalent one-way and two-way deterministic finite automata, from a descriptional complexity point of view.
We prove that for each one-way nondeterministic automaton with n states there exist Parikh equivalent one-way and two-way deterministic automata with e^O(sqrt(n lnn)) and p(n) states, respectively, where p(n) is a polynomial. Furthermore, these costs are tight. In contrast, if all the words accepted by the given one-way nondeterministic automaton contain at least two different letters, then a Parikh equivalent one-way deterministic automaton with a polynomial number of states can be found.
Concerning context-free grammars, we prove that for each grammar in Chomsky normal form with h variables there exist Parikh equivalent one-way and two-way deterministic automata with 2^O(h^2 ) and 2^O(h) states, respectively. Even these bounds are tight.
A further investigation is the study under Parikh equivalence of the state complexity of some language operations which preserve regularity. For union, concatenation, Kleene star, complement, intersection, shuffle, and reversal, we obtain a polynomial state complexity over any fixed alphabet, in contrast to the intrinsic exponential state complexity of some of these operations in the classical version. For projection we prove a superpolynomial state complexity, which is lower than the exponential one of the corresponding classical operation. We also prove that for each two one-way deterministic automata A and B it is possible to obtain a one-way deterministic automaton with a polynomial number of states whose accepted language has as Parikh image the intersection of the Parikh images of the languages accepted by A and B.
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Angelo, Maria Cristina. "The Gromov weak homotopy equivalence principle." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/13525/.
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The h-principle is a general homotopic way to solve partial differential equations and, more generally, partial differential relations. The theory was started by Y. Eliashberg, M. Gromov and A. V. Philips and it allows one to reduce a differential topological problem to an algebraic topological problem.
A way to prove the h-principle is by Convex Integration Theory. Developed originally by Gromov, it is applied to solve relations in jet spaces, including certain classes of undetermined non-linear systems of partial differential equations.
The h-principle occurs for instance in immersion problems, isometric immersion problems and other areas. A counter-intuitive result which can be proved by applying the h-principle is the sphere eversion without creasing or tearing.
This thesis consists of three parts. In the first chapter we introduce the concept of fiber bundle, which is a space that is locally a product space but globally may have a different topological structure, and the concept of jet bundle, a construction that makes a new smooth fiber bundle out of a given smooth fiber bundle. In the second chapter we develop the Gromov Convex Integration Theory that provides the main general topological method for solving the h-principle for a wide variety of problems in differential geometry and topology, with applications also to PDEs theory and to optimal control theory. Finally, in the last chapter, we examine some relations for which the h-principle holds.
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Dykstra, Andrew. "Two equivalence relations in symbolic dynamics." College Park, Md. : University of Maryland, 2007. http://hdl.handle.net/1903/6815.
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Thesis (Ph. D.) -- University of Maryland, College Park, 2007.Thesis research directed by: Mathematics. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.
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Ward-Robinson, Jasper. "An associative account of acquired equivalence." Thesis, University of York, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.319455.
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Fretwell, Paul. "Equivalence transformations in linear systems theory." Thesis, Loughborough University, 1986. https://dspace.lboro.ac.uk/2134/33259.
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There is growing interest in infinite frequency structure of linear systems, and transformations preserving this type of structure. Most work has been centred around Generalised State Space (GSS) systems. Two constant equivalence transformations for such systems are Rosenbrock's Restricted System Equivalence (RSE) and Verghese's Strong Equivalence (str.eq.). Both preserve finite and infinite frequency system structure. RSE is over restrictive in that it is constrained to act between systems of the same dimension. While overcoming this basic difficulty str.eq. on the other hand has no closed form description. In this work all these difficulties have been overcome. A constant pencil transformation termed Complete Equivalence (CE) is proposed, this preserves finite elementary divisors and non-unity infinite elementary divisors. Applied to GSS systems CE yields Complete System Equivalence (CSE) which is shown to be a closed form description of str.eq. and is more general than RSE as it relates systems of different dimensions. Equivalence can be described in terms of mappings of the solution sets of the describing differential equations together with mappings of the constrained initial conditions. This provides a conceptually pleasing definition of equivalence. The new equivalence is termed Fundamental Equivalence (FE) and CSE is shown to be a matrix characterisation of it. A polynomial system matrix transformation termed Full Equivalence (fll.e.) is proposed. This relates general matrix polynomials of different dimensions while preserving finite and infinite frequency structure. A definition of infinite zeros is also proposed along with a generalisation of the concept of infinite elementary divisors (IED) from matrix pencils to general polynomial matrices. The IED provide an additional method of dealing with infinite zeros.
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Ersson, Sara. "Code Clone Detection for Equivalence Assurance." Thesis, KTH, Skolan för elektroteknik och datavetenskap (EECS), 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-284329.
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To support multiple programming languages, the concept of offering applicationprogramming interfaces (APIs) in multiple programming languages hasbecome commonplace. However, this also brings the challenge of ensuringthat the APIs are equivalent regarding their interface. To achieve this, codeclone detection techniqueswere adapted to match similar function declarationsin the APIs. Firstly, existing code clone detection tools were investigated. Asthey did not perform well, a tree-based syntactic approach was used, where allheader files were compiled with Clang. The abstract syntax trees, which wereobtained during the compilation, were then traversed to locate the functiondeclaration nodes, and to store function names and parameter variable names.When matching the function names, a textual approach was used, transformingthe function names according to a set of implemented rules.A strict rule compares transformations of full function names in a preciseway, whereas a loose rule only compares transformations of parts of functionnames, and matches anything for the remainder. The rules were appliedboth by themselves, and in different combinations, starting with the strictestrule, followed by the second strictest rule, and so fourth.The best-matching rules showed to be the ones which are strict, and are notaffected by the order of the functions in which they are matched. These rulesshowed to be very robust to API evolution, meaning an increase in number ofpublic functions. Rules which are less strict and stable, and not robust to APIevolution, can still be used, such as matching functions on the first or last wordin the function names, but preferably as a complement to the stricter and morestable rules, when most of the functions already have been matched.The tool has been evaluated on the two APIs in King’s software developmentkit, and covered 94% of the 124 available function matches.För att stödja flera olika programmingsspråk har det blivit alltmer vanligt atterbjuda applikationsprogrammeringsgränssnitt (API:er) på olika programmeringsspråk.Detta resulterar dock i utmaningen att säkerställa att API:erna ärekvivalenta angående deras gränssnitt. För att uppnå detta har kodklonsdetekteringsteknikeranpassats, för att matcha liknande funktionsdeklarationeri API:erna. Först undersöktes existerande kodklonsverktyg. Eftersom de intepresterade bra, användes ett trädbaserat syntaktiskt tillvägagångssätt, där allaheader-filer kompilerades med Clang. De abstrakta syntaxträden, som erhöllsunder kompileringen, traverserades sedan för att lokalisera funktionsdeklarationsnoderna,och för att lagra funktionsnamnen och parametervariabelnamnen.När funktionsnamnen matchades, användes ett textbaserat tillvägagångssätt,som omvandlade funktionsnamnen enligt en uppsättning implementeraderegler.En strikt regel jämför omvandlingar av hela funktionsnamn på ett exakt sätt,medan en lös regel bara jämför omvandlingar av delar of funktionsnamn, ochmatchar den resterande delen med vadsomhelst. Reglerna applicerades bådasjälva och i olika kombinationer, där den striktaste regeln applicerades först,följt av den näst strikaste, och så vidare.De regler som matchar bäst visade sig vara de som är striktast, och som intepåverkas av ordningen på funktionerna i vilken de matchas. Dessa reglervisade sig vara väldigt robusta mot API-evolution, dvs. ett ökat antal publikafunktioner i API:erna. Regler som är mindre strikta och stabila, och interobusta mot API-evolution kan fortfarande användas, men helst som ett komplementtill de striktare och mer stabila reglerna, när de flesta av funktionernaredan har blivit matchade.Verktyget har evaluerats på de två API:erna i Kings mjukvaruutvecklarkit, ochtäckte 94% av de tillgängliga funktionsmatchningarna.
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Lee, Soonmook. "Model equivalence in covariance structure modeling /." The Ohio State University, 1987. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487327695623423.
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Clark, James Byron. "Fractional factorial designs-equivalence and augmenting /." The Ohio State University, 1998. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487949836206266.
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Jaber, Guilhem. "A logical study of program equivalence." Thesis, Nantes, Ecole des Mines, 2014. http://www.theses.fr/2014EMNA0124/document.
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Prouver l’équivalence de programmes écrits dans un langage fonctionnel avec références est un problème notoirement difficile. L’objectif de cette thèse est de proposer un système logique dans lequel de telles preuves peuvent être formalisées, et dans certains cas inférées automatiquement. Dans la première partie, une méthode générique d’extension de la théorie des types dépendants est proposée, basée sur une interprétation du forcing vu comme une traduction de préfaisceaux de la théorie des types. Cette extension dote la théorie des types de constructions récursives gardées, qui sont utilisées ensuite pour raisonner sur les références d’ordre supérieure. Dans une deuxième partie, nous définissons une sémantique des jeux nominale opérationnelle pour un langage avec références d’ordre supérieur. Elle marie la structure catégorique de la sémantique des jeux avec une représentation sous forme de traces de la dénotation des programmes, qui se calcule de manière opérationnelle et dispose donc de bonnes propriétés de modularité. Cette sémantique nous permet ensuite de prouver la complétude de relations logiques à la Kripke définit de manière directe, via l’utilisation de types récursifs gardés, sans utilisation de la biorthogonalité. Une telle définition directe nécessite l’utilisation de mondes omniscient et un contrôle fin des locations divulguées. Finalement, nous introduisons une logique temporelle qui donne un cadre pour définir ces relations logiques à la Kripke. Nous ramenons alors le problème de l’équivalence contextuelle à la satisfiabilité d’une formule de cette logique générée automatique, c’est à dire à l’existence d’un monde validant cette formule. Sous certaines conditions, cette satisfiabilité peut être décidée via l’utilisation d’un solveur SMT. La complétude de notre méthode devrait permettre d’obtenir des résultats de décidabilité pour l’équivalence contextuelle de certains fragment du langage considéré, en fournissant un algorithme pour construire de tels mondesProving program equivalence for a functional language with references is a notoriously difficult problem. The goal of this thesis is to propose a logical system in which such proofs can be formalized, and in some cases inferred automatically. In the first part, a generic extension method of dependent type theory is proposed, based on a forcing interpretation seen as a presheaf translation of type theory. This extension equips type theory with guarded recursive constructions, which are subsequently used to reason on higher-order references. In the second part, we define a nominal game semantics for a language with higher-order references. It marries the categorical structure of game semantics with a trace representation of denotations of programs, which can be computed operationally and thus have good modularity properties. Using this semantics, we can prove the completeness of Kripke logical relations defined in a direct way, using guarded recursive types, without using biorthogonality. Such a direct definition requires omniscient worlds and a fine control of disclosed locations. Finally, we introduce a temporal logic which gives a framework to define these Kripke logical relations. The problem of contextual equivalence is then reduced to the satisfiability of an automatically generated formula defined in this logic, i.e. to the existence of a world validating this formula. Under some conditions, this satisfiability can be decided using a SMT solver. Completeness of our methods opens the possibility of getting decidability results of contextual equivalence for some fragments of the language, by giving an algorithm to build such worlds
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Pllaha, Tefjol. "Equivalence of Classical and Quantum Codes." UKnowledge, 2019. https://uknowledge.uky.edu/math_etds/59.
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In classical and quantum information theory there are different types of error-correcting codes being used. We study the equivalence of codes via a classification of their isometries. The isometries of various codes over Frobenius alphabets endowed with various weights typically have a rich and predictable structure. On the other hand, when the alphabet is not Frobenius the isometry group behaves unpredictably. We use character theory to develop a duality theory of partitions over Frobenius bimodules, which is then used to study the equivalence of codes. We also consider instances of codes over non-Frobenius alphabets and establish their isometry groups. Secondly, we focus on quantum stabilizer codes over local Frobenius rings. We estimate their minimum distance and conjecture that they do not underperform quantum stabilizer codes over fields. We introduce symplectic isometries. Isometry groups of binary quantum stabilizer codes are established and then applied to the LU-LC conjecture.
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Yang, Zhenkun. "Scalable Equivalence Checking for Behavioral Synthesis." PDXScholar, 2015. https://pdxscholar.library.pdx.edu/open_access_etds/2461.
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Behavioral synthesis is the process of compiling an Electronic System Level (ESL) design to a register-transfer level (RTL) implementation. ESL specifications define the design functionality at a high level of abstraction (e.g., with C/C++ or SystemC), and thus provide a promising approach to address the exacting demands to develop feature-rich, optimized, and complex hardware systems within aggressive time-to-market schedules. Behavioral synthesis entails application of complex and error-prone transformations during the compilation process. Therefore, the adoption of behavioral synthesis highly depends on our ability to ensure that the synthesized RTL conforms to the ESL description. This dissertation provides an end-to-end scalable equivalence checking support for behavioral synthesis. The major challenge of this research is to bridge the huge semantic gap between the ESL and RTL descriptions, which makes the direct comparison of designs in ESL and RTL difficult. Moreover, a large number and a wide variety of aggressive transformations from front-end to back-end require an end-to-end scalable checking framework.
This dissertation provides an end-to-end scalable equivalence checking support for behavioral synthesis. The major challenge of this research is to bridge the huge semantic gap between the ESL and RTL descriptions, which makes the direct comparison of designs in ESL and RTL difficult. Moreover, a large number and a wide variety of aggressive transformations from front-end to back-end require an end-to-end scalable checking framework.
A behavioral synthesis flow can be divided into three major phases, including 1) front-end : compiler transformations, 2) scheduling: assigning each operation a clock cycle and satisfying the user-specified constraints, and 3) back-end : local optimizations and RTL generation. In our end-to-end and incremental equivalence checking framework, we check each of the three phases one by one. Firstly, we check the front-end that consists of a sequence of compiler transformations by decomposing it into a series of checks, one for each transformation applied. We symbolically explore paths in the input and output programs of each transformation, and check whether the input and output programs have the same observable behavior under the same path condition. Secondly, we validate the scheduling transformation by checking the preservation of control and data dependencies, and the preservation of I/O timing in the user-specified scheduling mode. Thirdly, we symbolically simulate the scheduled design and the generated RTL cycle by cycle, and check the equivalence of each mapped variables. We also develop several key optimizations to make our back-end checker scale to real industrial-strength designs. In addition to the equivalence checking framework, we also present an approach to detecting deadlocks introduced by parallelization of RTL blocks that are connected by synthesized interfaces with handshaking protocols.
To demonstrate the efficiency and scalability of our framework, we evaluated it on transformations applied by a behavioral synthesis tool to designs from the C-based CHStone and SystemC-based S2CBench benchmarks. Based on the evaluation results, our front-end checker can efficiently validate more than 75 percent of the total of 1008 compiler transformations applied to designs from the CHStone benchmark, taking an average time of 1.5 seconds per transformation. Our scheduling checker can validate control-data dependencies and I/O timing of all designs from S2CBench benchmark. Our back-end checker can handle designs with more than 32K lines of synthesized RTL from the CHStone benchmark, which demonstrates the scalability of the checker. Furthermore, our checker found several bugs in a commercial tool, underlining both the importance of formal equivalence checking and the effectiveness of our approach.
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Roux, Karen. "Examining the equivalence of the PIRLS 2016 released texts in South Africa across three languages." Thesis, University of Pretoria, 2020. http://hdl.handle.net/2263/80509.
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The Progress in International Reading Literacy Study (PIRLS) is a large-scale reading comprehension assessment, which assesses Grade 4 learners’ reading literacy achievement. The findings from the last cycle of PIRLS 2016 indicated that South African Grade 4 and 5 learners performed poorly in reading comprehension. This finding confirms the previous cycles’ results where South African learners achieved the lowest results across the participating countries. Approximately eight out of ten Grade 4 learners cannot read for meaning in any of the tested languages. Due to the poor results in PIRLS, the President of South Africa stated that every ten-year old child should be able to read for meaning, thus cementing reading literacy as a national aim. The aim of this mixed methods research was to determine whether the PIRLS Literacy 2016 and PIRLS 2016 limited release texts are equivalent across languages, specifically English, Afrikaans and isiZulu.
Four research sub-questions were explored to assist in addressing the main research question posed by this study: To what extent are the PIRLS 2016 released texts in English, Afrikaans and isiZulu, in Grade 4 and Grade 5 equivalent? As this study took the form of a sequential explanatory mixed methods approach, the first phase investigated the South African Grade 4 and 5 results by firstly looking at descriptive statistics, such as percentages and means. After the initial exploration of the data, I conducted Rasch analyses to determine whether the items from the limited release texts showed measurement invariance – in other words, whether the items behaved differently for different groups of learners. As part of the Rasch analyses, individual item-fit statistics and differential item functioning (DIF) were conducted using RUMM2030. In phase two, the limited release texts were analysed by experts who attended workshops and completed open-ended questionnaires regarding the equivalence of the identified texts. The qualitative phase was conducted in order to complement and extend on the quantitative findings of phase one.
The findings revealed that the limited release texts, with their accompanying items, were not equivalent across the different languages. However, by looking at the items that displayed DIF, there is not a clear pattern as the items did not universally favour one language nor did the texts discriminate universally against a particular language. An in-depth look at the texts and items themselves revealed that the Flowers on the Roof text is considered the poorest translation into Afrikaans and isiZulu. Overall, all the texts were considered to be appropriate for South African learners as the texts made use of rich vocabulary and introduced the learners to new ideas and concepts. Thus, this study offers new insights into the equivalence of the PIRLS assessments as well as possible reasons for the non-equivalence for each of the limited release texts. Based on the findings of this study, recommendations and further research are provided.Thesis (PhD)--University of Pretoria, 2020.
Science, Mathematics and Technology Education
PhD
Unrestricted
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Zavala-Rojas, Diana. "Measurement equivalence in multilingual comparative survey research." Doctoral thesis, Universitat Pompeu Fabra, 2016. http://hdl.handle.net/10803/399146.
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The present dissertation explores language effects in a comparative survey i.e. to what extent linguistic diversity affects equivalence in a comparative survey. This is done by studying three different dimensions on the challenges of designing a comparative multilingual survey: survey translation, linguistically diverse countries and bilingualism. Guidelines in survey translation do not link assessment criteria and measurement equivalence testing. I propose a systematic procedure to compare versions of a question in different languages before fieldwork which establishes that link. In linguistically diverse countries, survey instruments are translated into more than one language, equivalence is commonly assumed, not tested. I test for invariance distinguishing the response and cognitive processes to a survey question. Finally, I study measurement equivalence within an individual in two languages for political constructs (bilingualism), challenging current methodological approaches by bringing latent variable models.
In each dimension, findings aim to contribute to improving comparative survey methodology.Esta tesis explora los efectos del lenguaje en una encuesta comparativa: en qué medida la diversidad lingüística afecta la equivalencia de los datos mediante el estudio de tres dimensiones: la traducción de encuestas, países lingüísticamente diversos y el bilingüismo. Las directrices actuales en la traducción de encuestas no vinculan los criterios de evaluación con un test de equivalencia. Se propone un procedimiento sistemático para comparar las versiones de una pregunta que establece dicho vínculo, en diferentes idiomas antes del trabajo de campo. En países lingüísticamente diversos, el cuestionario se traduce en más de un idioma. Se realiza un test de equivalencia que permite distinguir los procesos de respuesta de los cognitivos. Finalmente, se estudia la equivalencia de conceptos políticos en dos idiomas para un individuo (bilingüismo), proponiendo un enfoque metodológico de modelos de variables latentes. Los hallazgos tienen por objeto contribuir a mejorar la metodología de encuestas en estudios comparativos.
Aquesta tesi explora els efectes del llenguatge en una enquesta comparativa: en quina mesura la diversitat lingüística afecta l'equivalència de les dades; mitjançant l'estudi de tres dimensions: la traducció d'enquestes, els països lingüísticament diversos i el bilingüisme. Les directrius actuals en la traducció d'enquestes no vinculen els criteris d'avaluació amb un test d'equivalència de mesures. Per tant, es proposa un procediment sistemàtic que estableix aquest vincle per comparar les versions d'una pregunta en diferents idiomes abans del començament del traball de camp. En països lingüísticament diversos, el qüestionari es tradueix en més d'un idioma. A la tesi, es realitza un test d'equivalència que permet diferenciar els processos de resposta dels cognitius. Finalment, s'estudia l'equivalència de conceptes polítics pel mateix individu en els seus dos idiomes (bilingüisme), mitjançant l’aplicació de models amb variables latents. Els resultats tenen per objectiu contribuir a millorar la metodologia d'enquestes en estudis comparatius.
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Preuss, Oliver. "Astronomical tests of the Einstein equivalence principle." [S.l. : s.n.], 2002. http://deposit.ddb.de/cgi-bin/dokserv?idn=966610180.
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Dahl, Heidi. "Cantor minimal systems and AF-equivalence relations." Doctoral thesis, Norwegian University of Science and Technology, Faculty of Information Technology, Mathematics and Electrical Engineering, 2008. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-1897.
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Guyonnet, Dominique. "Equivalence en Etanchéité Minérale : Caractérisation et Prévision." Habilitation à diriger des recherches, INSA de Lyon, 2003. http://tel.archives-ouvertes.fr/tel-00578923.
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Le thème fédérateur de mes travaux de recherche passés et en cours est : la prévention et la prévision de l'impact de sources de pollution sur le sous-sol. Ce thème général a été décliné suivant plusieurs axes de recherche : a) Résolution des équations de bilan de masse décrivant la migration des polluants dans l'eau souterraine, b) Caractérisation des barrières minérales pour le confinement des déchets, c) Comportement des déchets à la lixiviation, d) Prise en compte de l'incertitude dans l'évaluation du risque d'exposition aux polluants du sol.
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Pomet, Jean-Baptiste. "Equivalence et Linearisation des systèmes de contrôle." Habilitation à diriger des recherches, Université de Nice Sophia-Antipolis, 2009. http://tel.archives-ouvertes.fr/tel-00429825.
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Les modèles de systèmes de contrôle en dimension finie et en temps continu sont les équations différentielles ordinaires sous-déterminées, c'est-à-dire prescrivant l'évolution d'une partie des variables alors que d'autres, les contrôles, sont libres. Cette sous-détermination fait que la classe de transformations possibles est très variée et que le problème est par exemple très différent de celui des systèmes dynamiques classiques (sans contrôle, ou équations différentielles ordinaires déterminées). On a fait, dans le chapitre 1 (le seul original) un effort de clarification des différents types de transformations (statiques, dynamiques, fonctionnelles..) en les énonçant en terme de correspondances entre solutions; on présente ensuite des contributions des dernières années, concernant des conditions géométriques d'équivalence ou de linéarisation, et des problèmes encore ouverts; les détails sont contenus dans huit articles publiés reproduits dans le mémoire aux chapitres suivants (en anglais) avec seulement quelques modifications de référencement.
Étudier la structure des transformations sur les modèles, leur équivalence, leur classification a deux motivations distinctes:
- pour concevoir un contrôleur à partir d'un modèle donné du système, on a souvent intérêt à analyser, comprendre, simplifier ce modèle,
- le choix d'un modèle demande une compréhension de la structure de la classe des modèles non-linéaires (par exemple: quand deux modèles traduisent-ils la même réalité?). La modélisation ou l'identification non-linéaires sont encore des champs en friche qui manquent de fondements conceptuels.
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Helgstrand, Charlotte. "Control of Quasi-Equivalence in Virus Capsids." Doctoral thesis, Uppsala universitet, Institutionen för cell- och molekylärbiologi, 2002. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-2694.
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Many T=3 plant and insect viruses use a molecular switch in form of order/disorder of a segment of the polypeptide chain to regulate the quasi-equivalent contacts. The structure of a mutant of the T=3 capsid of bacteriophage fr confirms that this virus and other members of the Leviviridae family lack a switch mechanism. The geometric principles underlying the construction of spherical virus capsid do not allow more than 60 protein monomers to from a capsid while maintaining an identical chemical environment. Most virus capsid, however, contain many more protein subunits. Quasi-equivalence explains how the capsid proteins can have slightly different interactions in the virus shell. Quasi-equivalence requires the capsids to be constructed from multiples of 60 subunits, where the T number denotes the multiplicity. The structure of the T=4 Nudaurelia capensis ω Virus shows a molecular switch in form of a C-terminal helix inserted in some contacts between protein dimers. This virus is very similar in structure to the T=3 nodaviruses. In the nodaviruses a five-membered helix bundle, formed by cleaved peptides around the five-fold axes on the inside of the shell, are suggested to aid in membrane translocation of the genomic RNA. In Nudaurelia capensis ω Virus the helix bundle is formed by 10 helices, of which 5 are still covalently attached to the capsid proteins. Bacteriophage HK97 has T=7 quasi-symmetry. A domain that is degraded during maturation and is not present in the structure of the mature virion controls the quasi-equivalence. During maturation covalent bonds are formed between the protein subunits, producing a set of interlocking covalently bound rings, resembling chainmail. Structural studies of complexes between the bacteriophage MS2 and variants of its translational operator are also included in this work. A dimer of the MS2 coat protein binds with sequence specificity to an operator in its genomic RNA, and causes translational repression. Structures of multiple RNA segments with altered sequence at some positions which are required for binding to the capsid protein, has been determined.
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Haug, Alfred A. (. "Ricardian equivalence or debt illusion : empirical studies /." Connect to resource, 1987. http://rave.ohiolink.edu/etdc/view.cgi?acc%5Fnum=osu1267621324.
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Schröder, Carsten. "Variable income equivalence scales : an empirical approach /." Heidelberg : Physica-Verl, 2004. http://www.loc.gov/catdir/enhancements/fy0813/2004102143-d.html.
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Zahedi, Ashkan. "Equivalence problems for Lagrangians on the line." Thesis, McGill University, 2004. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=81460.
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We review Cartan's method for determining whether two G-structures are locally equivalent. This method is based on the reduction of the structure group to the identity, giving rise to a complete set of local invariants. There are several techniques such as group reduction, prolongation, involutivity test, absorbtion of torsion, and normalization needed in this procedure. Next we introduce the equivalence problem for first-order Lagrangians on the line. We apply this method to the solution of the equivalence problem for the first order Lagrangians under fiber-preserving transformations, point transformations, fiber-preserving transformations up to a divergence, and point transformations up to a divergence. All the local invariants are explicitly computed.
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Galpin, Vashti C. "Equivalence semantics for concurrency : comparison and application." Thesis, University of Edinburgh, 1998. http://hdl.handle.net/1842/389.
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Since the development of CCS and other process algebras, many extensions to these process algebras have been proposed to model different aspects of concurrent computation. It is important both theoretically and practically to understand the relationships between these process algebras and between the semantic equivalences that are defined for them. In this thesis, I investigate the comparison of semantic equivalences based on bisimulation which are defined for process algebras whose behaviours are described by structured operational semantics, and expressed as labelled transition systems. I first consider a hierarchy of bisimulations for extensions to CCS, using both existing and new results to describe the relationships between their equivalences with respect to pure CCS terms. I then consider a more general approach to comparison by investigating labelled transition systems with structured labels. I define bisimulation homomorphisms between labelled transition systems with different labels, and show how these can be used to compare equivalences. Next, I work in the meta-theory of process algebras and consider a new format that is an extension of the tyft/tyxt format for transition system specifications. This format treats labels syntactically instead of schematically, and hence I use a definition of bisimulation which requires equivalence between labels instead of exact matching. I show that standard results such as congruence and conservative extension hold for the new format. I then investigate how comparison of equivalences can be approached through the notion of extension to transition system specifications. This leads to the main results of this study which show how in a very general fashion the bisimulations defined for two different process algebras can be compared over a subset of terms of the process algebras. I also consider what implications the conditions which are required to obtain these results have for modelling process algebras, and show that these conditions do not impose significant limitations. Finally, I show how these results can be applied to existing process algebras. I model a number of process algebras with the extended format and derive new results from the meta-theory developed.
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Robbins, Daniel Stephen. "A derived Equivalence for the Tits Group." Thesis, University of Bristol, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.499894.
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Purdie, Craig. "Deflection of light with the equivalence principle." Thesis, University of Canterbury. Physics and Astronomy, 1997. http://hdl.handle.net/10092/7939.
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A thorough treatment of the Strong Equivalence Principle is presented, demonstrating its failure in dealing with non-uniform gravitational fields. In particular, a calculation utilising the equivalence principle is shown to produce an incorrect rate of deflection of light. This calculation is used as a tool to investigate the nature of this deflection, and the meaning of the Strong Equivalence Principle.
Using a generalised metric for outside a static, spherically symmetric gravitational source, it is shown that the failure of the equivalence principle is geometric and not due to any particular choice of metric. When transformed into a displaced rectangular coordinate system, the generalised metric consists of both diagonal and off-diagonal elements. Only the diagonal elements are equivalent to a flat, uniformly accelerating frame. The off-diagonal elements produce non-zero elements in the Riemann Curvature Tensor and are thus attributed to curvature. Therefore, the Strong Equivalence principle is only valid in the weak field limit, where the components of the Riemann curvature tensor vanish. In this case the metric becomes flat, which is the equivalent of a uniform gravitational field.
Using the Schwarzschild metric in displaced rectangular coordinates, the effect of curvature on the rate of deflection of light are determined by tracing the effect of the off-diagonal elements. This calculation shows that only one-third of the deflection rate is due to acceleration in the local inertial frame, with the remaining two-thirds being the result of curvature. Because the rate of deflection is is an infinitesimal quantity defined locally, this shows the effects of curvature are important even for local measurements.
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Barra, Aleams. "Equivalence Theorems and the Local-Global Property." UKnowledge, 2012. http://uknowledge.uky.edu/math_etds/5.
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In this thesis we revisit some classical results about the MacWilliams equivalence theorems for codes over fields and rings. These theorems deal with the question whether, for a given weight function, weight-preserving isomorphisms between codes can be described explicitly. We will show that a condition, which was already known to be sufficient for the MacWilliams equivalence theorem, is also necessary. Furthermore we will study a local-global property that naturally generalizes the MacWilliams equivalence theorems. Making use of F-partitions, we will prove that for various subgroups of the group of invertible matrices the local-global extension principle is valid.
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Al-Dulaimi, J. J. M. "A study of power system network equivalence." Thesis, University of Glasgow, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.381329.
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McGuigan, Sean. "Emergent rule following and functional equivalence classes." Thesis, University of Ulster, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.274555.
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Park, Sung Min S. M. Massachusetts Institute of Technology. "On the equivalence of sparse statistical problems." Thesis, Massachusetts Institute of Technology, 2016. http://hdl.handle.net/1721.1/107375.
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Thesis: S.M., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2016.Cataloged from PDF version of thesis.
Includes bibliographical references (pages 43-47).
Sparsity is a widely used and theoretically well understood notion that has allowed inference to be statistically and computationally possible in the high-dimensional setting. Sparse Principal Component Analysis (SPCA) and Sparse Linear Regression (SLR) are two problems that have a wide range of applications and have attracted a tremendous amount of attention in the last two decades as canonical examples of statistical problems in high dimension. A variety of algorithms have been proposed for both SPCA and SLR, but their literature has been disjoint for the most part. We have a fairly good understanding of conditions and regimes under which these algorithms succeed. But is there be a deeper connection between computational structure of SPCA and SLR? In this paper we show how to efficiently transform a blackbox solver for SLR into an algorithm for SPCA. Assuming the SLR solver satisfies prediction error guarantees achieved by existing efficient algorithms such as those based on the Lasso, we show that the SPCA algorithm derived from it achieves state of the art performance, matching guarantees for testing and for support recovery under the single spiked covariance model as obtained by the current best polynomial-time algorithms. Our reduction not only highlights the inherent similarity between the two problems, but also, from a practical standpoint, it allows one to obtain a collection of algorithms for SPCA directly from known algorithms for SLR. Experiments on simulated data show that these algorithms perform well.
by Sung Min Park.
S.M.
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Ardeshir-Larijani, Ebrahim. "Automated equivalence checking of quantum information systems." Thesis, University of Warwick, 2014. http://wrap.warwick.ac.uk/63940/.
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Quantum technologies have progressed beyond the laboratory setting and are beginning to make an impact on industrial development. The construction of practical, general purpose quantum computers has been challenging, to say the least. But quantum cryptographic and communication devices have been available in the commercial marketplace for a few years. Quantum networks have been built in various cities around the world, and plans are afoot to launch a dedicated satellite for quantum communication. Such new technologies demand rigorous analysis and verification before they can be trusted in safety and security-critical applications. In this thesis we investigate the theory and practice of equivalence checking of quantum information systems. We present a tool, Quantum Equivalence Checker (QEC), which uses a concurrent language for describing quantum systems, and performs verification by checking equivalence between specification and implementation. For our process algebraic language CCSq, we define an operational semantics and a superoperator semantics. While in general, simulation of quantum systems using current computing technology is infeasible, we restrict ourselves to the stabilizer formalism, in which there are efficient simulation algorithms and representation of quantum states. By using the stabilizer representation of quantum states we introduce various algorithms for testing equality of stabilizer states. In this thesis, we consider concurrent quantum protocols that behave functionally in the sense of computing a deterministic input-output relation for all interleavings of a concurrent system. Crucially, these input-output relations can be abstracted by superoperators, enabling us to take advantage of linearity. This allows us to analyse the behaviour of protocols with arbitrary input, by simulating their operation on a finite basis set consisting of stabilizer states. We present algorithms for the checking of functionality and equivalence of quantum protocols. Despite the limitations of the stabilizer formalism and also the range of protocols that can be analysed using equivalence checking, QEC is applied to specify and verify a variety of interesting and practical quantum protocols from quantum communication and quantum cryptography to quantum error correction and quantum fault tolerant computation, where for each protocol different sequential and concurrent model are defined in CCSq. We also explain the implementation details of the QEC tool and report on the experimental results produced by using it on the verification of a number of case studies.
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Cotton, Michael R. "Abelian Group Actions and Hypersmooth Equivalence Relations." Thesis, University of North Texas, 2019. https://digital.library.unt.edu/ark:/67531/metadc1505289/.
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We show that any Borel action on a standard Borel space of a group which is topologically isomorphic to the sum of a countable abelian group with a countable sum of lines and circles induces an orbit equivalence relation which is hypersmooth. We also show that any Borel action of a second countable locally compact abelian group on a standard Borel space induces an orbit equivalence relation which is essentially hyperfinite, generalizing a result of Gao and Jackson for the countable abelian groups.
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West, Jennifer L. "TELEHEALTH PARENT TRAINING FOR EQUIVALENCE BASED INSTRUCTION." OpenSIUC, 2020. https://opensiuc.lib.siu.edu/theses/2765.
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AN ABSTRACT OF THE THESIS OFJennifer L. West, for the Master of Science degree in Applied Behavior Analysis, presented on June 22, 2020, at Southern Illinois University Carbondale. TITLE: TELEHEALTH PARENT TRAINING FOR EQUIVALENCE BASED INSTRUCTIONMAJOR PROFESSOR: Dr. Mark Dixon The purpose of the present study was to evaluate the effectiveness of teaching derived geographic skills to two children with disabilities through the use of conditional discrimination training and testing procedures. A multiple baseline across subjects was used in which non-reinforced probes were initially taken across six different stimulus relations. Afterwards various series of trial blocks of conditional discrimination training for the A-B and B-C relations occurred, as well as tests for the C-D derived relations. Performance rose above baseline levels. Implications for caretakers are provided suggesting that with remote guidance caretakers can effectively administer such interventions to persons with disabilities. KEYWORDS: Equivalence based instruction, Telehealth, Autism Spectrum Disorder, Parent Training.
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Haug, Alfred A. ""Ricardian equivalence or debt illusion : empirical studies"." The Ohio State University, 1987. http://rave.ohiolink.edu/etdc/view?acc_num=osu1267621324.
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Peacock, Simon F. "On separable equivalence of finite dimensional algebras." Thesis, University of Bristol, 2015. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.688100.
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Separable equivalence of algebras was introduced by Markus Linckelmann in [Linllb] and may be considered as an extension to the more well-known concepts of Morita, stable and derived equivalence. We will generalise the idea of separable equivalence of algebras to additive categories and demonstrate how a separable equivalence between algebras provides separable equivalences between several related categories. We will prove that there are several properties of an algebra that are invariant under separable equivalence. Specifically we show that if two algebras are separably equivalent then they must have the same complexity. We also show that the representation type of an algebra is preserved, including the finer grain classes of domestic and polynomial growth. Finally, if G is a finite group with elementary abelian Sylow p-subgroup P, then we use the separable equivalence of kG and kP to provide an upper bound for the representation dimension of kG, where k is an algebraically closed field of characteristic p.