Submitted by CAROLINE DE ARRUDA SIGNORINI null (carolineasignorini@gmail.com) on 2017-03-22T17:30:47Z No. of bitstreams: 1 Dissertação - versão definitiva [22.03.2017].pdf: 1265324 bytes, checksum: cb95983dd59698aa1bb765a4dd7f9866 (MD5) / Approved for entry into archive by Luiz Galeffi (luizgaleffi@gmail.com) on 2017-03-23T13:46:47Z (GMT) No. of bitstreams: 1 signorini_ca_me_sjrp.pdf: 1265324 bytes, checksum: cb95983dd59698aa1bb765a4dd7f9866 (MD5) / Made available in DSpace on 2017-03-23T13:46:47Z (GMT). No. of bitstreams: 1 signorini_ca_me_sjrp.pdf: 1265324 bytes, checksum: cb95983dd59698aa1bb765a4dd7f9866 (MD5) Previous issue date: 2017-03-07 / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Nosso principal propósito neste trabalho é o estudo de condições necessárias e suficientes de otimalidade para problemas de Cálculo das Variações no contexto não-suave. Este estudo partirá da formulação básica suave, passando por problemas com restrições Lagrangianas, até o caso em que consideramos Lagrangianas não-suaves e soluções absolutamente contínuas. Neste caminho, abordaremos um importante avanço na teoria de Cálculo das Variações: os resultados de existência e regularidade de soluções. Além das condições necessárias, analisaremos as condições suficientes através de um conceito de convexidade generalizada, o qual denominamos E-pseudoinvexidade. / Our main purpose in this work is the study of necessary and sufficient optimality conditions for Calculus of Variations problems in the nonsmooth context. This study will comprehend the smooth basic formulation, constrained problems (with Lagrangian restrictions), non-smooth Lagrangians and absolutely continuous solutions. Moreover, we will approach an important advance in Calculus of Variations theory: the existence and regularity of solutions. In addition to necessary conditions, we will analyze sufficient conditions through a generalized convexity concept, which we called E-pseudoinvexity. / FAPESP: 2014/24271-6

This thesis attempts to provide a coherent view of the idea of ‘justice as fairness’ and, in particular, the ‘difference principle’ expressed by John Rawls in A Theory of Justice. The main focus of the thesis is the difference principle and its limits. Rawls’s conception of ‘justice as fairness’ is based on the thought experiment of the ‘original position’ in which people, considered as free and equal, deliberate under an imagined ‘veil of ignorance,’ i.e. not knowing which social roles or status they would occupy in their society. Rawls then argues that in the original position people come up with two major principles of justice, understood as principles that would be acceptable to people treated as free and equal. The second principle entails the so-called ‘difference principle,’ according to which the inequalities of, say, wealth and authority are just and fair only if they lead to compensating benefits for everybody and particularly the least advantaged. The thesis proceeds, then, by probing whether compared with other theories, , including a discussion of Dahl’s theory of democracy, Rawls’s difference principle could be a proper answer to one of the main questions of social justice. The questions is: how the economic fortune in a society should be distributed among citizens. However, despite Rawls’s aim to develop the difference principle as a practical normative theory, it fails to give us a pragmatic answer. The reason is: the statement of the difference principle fails to take into account one crucial point: to wit, the matter of time. The thesis develops two empirical economic scenarios to illustrate that there is a trade-off between the interests of the poor in short and long period of time. However, this important issue is not considered and discussed by Rawls which makes the theory inapplicable.

Wir studieren das Verhalten des Maximums, des Minimums und des Endwerts zeithomogener eindimensionaler Diffusionen auf endlichen Zeitintervallen. Zuerst beweisen wir mit Hilfe des Malliavin-Kalküls ein Existenzresultat für die gemeinsamen Dichten. Außerdem leiten wir Entwicklungen der gemeinsamen Momente des Tripels (H,L,X) zur Zeit Delta bzgl. Delta her. Dabei steht X für die zugrundeliegende Diffusion, und H und L bezeichnen ihr fortlaufendes Maximum bzw. Minimum. Ein erster Ansatz, der vollständig auf den elementaren Abschätzungen der Doob’schen und der Cauchy-Schwarz’schen Ungleichung beruht, liefert eine Entwicklung bis zur Ordnung 2 bzgl. der Wurzel der Zeitvariablen Delta. Ein komplexerer Ansatz benutzt Partielle-Differentialgleichungstechniken, um eine Entwicklung der einseitigen Austrittswahrscheinlichkeit für gepinnte Diffusionen zu bestimmen. Da eine Entwicklung der Übergangsdichten von Diffusionen bekannt ist, erhält man eine vollständige Entwicklung der gemeinsamen Wahrscheinlichkeit von (H,X) bzgl. Delta. Die entwickelten Verteilungseigenschaften erlauben es uns, eine Theorie für Martingalschätzfunktionen, die aus wertebereich-basierten Daten konstruiert werden, in einem parameterisierten Diffusionsmodell, herzuleiten. Ein Small-Delta-Optimalitätsansatz, der die approximierten Momente benutzt, liefert eine Vereinfachung der vergleichsweise komplizierten Schätzprozedur und wir erhalten asymptotische Optimalitätsresultate für gegen 0 gehende Sampling-Frequenz. Beim Schätzen des Drift-Koeffizienten ist der wertebereich-basierte Ansatz der Methode, die auf equidistanten Beobachtungen der Diffusion beruht, nicht überlegen. Der Effizienzgewinn im Fall des Schätzens des Diffusionskoeffizienten ist hingegen enorm. Die Maxima und Minima in die Analyse miteinzubeziehen senkt die Varianz des Schätzers für den Parameter in diesem Szenario erheblich. / We study the behavior of the maximum, the minimum and the terminal value of time-homogeneous one-dimensional diffusions on finite time intervals. To begin with, we prove an existence result for the joint density by means of Malliavin calculus. Moreover, we derive expansions for the joint moments of the triplet (H,L,X) at time Delta w.r.t. Delta. Here, X stands for the underlying diffusion whereas H and L denote its running maximum and its running minimum, respectively. In a first approach that entirely relies on elementary estimates, such as Doob’s inequality and Cauchy-Schwarz’ inequality, we derive an expansion w.r.t. the square root of the time parameter Delta including powers of 2. A more sophisticated ansatz uses partial differential equation techniques to determine an expansion of the one-barrier hitting time probability for pinned diffusions. For an expansion of the transition density of diffusions is known, one obtains an overall expansion of the joint probability of (H,X) w.r.t. Delta. The developed distributional properties enable us to establish a theory for martingale estimating functions constructed from range-based data in a parameterized diffusion model. A small-Delta-optimality approach, that uses the approximated moments, yields a simplification of the relatively complicated estimating procedure and we obtain asymptotic optimality results when the sampling frequency Delta tends to 0. When it comes to estimating the drift coefficient the range-based method is not superior to the method relying on equidistant observations of the underlying diffusion alone. However, there is an enormous gain in efficiency at the estimation for the diffusion coefficient. Incorporating the maximum and the minimum into the analysis significantly lowers the asymptotic variance of the estimators for the parameter in this scenario.

實驗設計中，我們假設在區塊中存在一趨勢效應(trend effect)。此趨勢效應影響觀察值，也影響我們對區塊效應(block effect)和處理效應(treatment effect)的估計。此種設計模式不同於一般的區塊設計模式，因此須將趨勢效應加人設計模式中。 　　Bradley and Yeh (1980)研究和討論此種趨勢效應在區塊設計模式中之影響，並定義出無趨勢設計(trend-free design)。所謂無趨勢設計，乃是在區塊設計模式中，趨勢效應被抵消不影響處理效應之分析。Bradley and Yeh (1983)推導了一個線性無趨勢設計存在的必要條件是r(k+1)≡0(mod 2)其中k為區塊大小，r為處理出現的次數。 　　Bradley and Yeh進一步預測任一滿足r(k+1)≡0(mod2)的區塊設計，經過在區塊中處理位置調整後，可變為一個線性無趨勢設計。本篇論文的主要目的乃是在探討給定一GD設計(group-divisibledesigns)，檢驗和推導此預測是否為真。 / Yeh and Bradley conjectured that every binary connected block design with blocks of size k and a constant replication numberr for each treatment can be converted to a linear trend-free design by permuting the positions of theatments within blocks if and only if r(k+1)≡0 (mod 2). Chai and Majumdar (1993) proved that any BIB design which satisfies r(k+1)≡0 (mod 2) is even can be converted to a linear trend-free design. In this thesis, we want to examine this conjecture is true or not for group-divisible designs (GD designs).

本文以優選理論為框架探討閩南語三字組及四字組重疊構詞，三字組及四字組重疊構詞可分成完全重疊與部分重疊，重疊詞要緊鄰其對應詞基越好，此外，對於四字組部分重疊構詞有對整方向不一致的體現，筆者認為不同的制約排序會產生不同的重疊規則，並採用音韻共存理論(Cophonology Theory)來解釋閩南語多元的重疊構詞策略是由多個次語法運作的結果。在三字組重疊構詞，根據句法結構判斷主重音的位置，主重音的分佈影響重疊的規則，但有語意強調某成份時，主重音會轉移且會使原成份之本調喪失變成輕聲，有主重音的音節才可進行重疊構詞，同時，重疊詞要越緊鄰其對應詞基。在四字組完全重疊構詞，語義的強調與弱化影響詞基音節以及音步的重疊運作，音節與音步制約層級不同可解釋不同的重疊規則；在四字組部分重疊構詞，不同於過去研究以單一方向對整制約論證，筆者提出雙向的對整制約來解釋四字組部分重疊構詞。簡言之，本篇論文藉由優選理論的觀點，首度就閩南語重疊構詞提出一個整體分析。 / This thesis examines the derivation of the reduplication in Taiwan Southern Min under the framework of Optimality Theory. Reduplication can be divided into two categories. One is trisyllabic reduplication and the other is quadrisyllabic reduplication. Besides, each type of the trisyllabic and quadrisyllabic reduplication has both partial and full reduplication. This thesis adopts Cophonology Theory to account for the subgrammar of the divergent reduplications. Based on Locality Generalization, the reduplicant should be adjacent to its corresponding base. In trisyllabic reduplication, from the perspective of syntactic relation, stress affects the derivation of the reduplication. The primary stressed syllable is the only syllable which can be reduplicated. This thesis proposes constraint *RED(W) to require this condition. In quadrisyllabic reduplication, given the base is disyllable AB, semantic weakness and stress closely relate to the full reduplication AABB and ABAB. The different ranking of the Adjacency-BR-by-syllable and Adjacency-BR-by-foot explains the full reduplication. In quadrisyllabic partial reduplication, this thesis proposes the different edges alignment constraint Align(RED, R; Rightmost Monosyllabic Morpheme, L) and Align(RED, L; Leftmost Monosyllabic Morpheme, R) to explain ABAC and ACBC, respectively. In summary, based on the constraint-based theory, and the interaction of Nonhead stress, Focal stress, *RED(W), alignment, anchoring, adjacency, and contiguity constraint, this thesis has given a general explanation of the reduplication in Taiwan Southern Min.

本文以優選理論的觀點分析美濃客語的陰平變調。討論可分為兩部分，首先，針對於變調的範疇，文章從句法與音韻的介面關係探討陰平變調的範疇，結果顯示陰平變調是以語調詞組(Intonational Phrase)作為變調的範疇，而這也為韻律結構的存在提供了證據。語調詞組的形成與感知單位(Sense Unit Condition)和重組(Restructuring)有密切的關係。另外，也探討了語調詞組中的特殊結構，發現語料支持Nespor & Vogel (1986)的假設，即特殊結構可以先形成一個獨立的語調詞組。 探討完變調範疇之後，將以優選理論進行分析。本文提出兩組制約:聲調制約和韻律制約。聲調制約著重在解釋變調的運作，而韻律制約則負責解釋變調範疇的劃分，這兩組制約不僅能解釋一般句子的變調，亦能對特殊結構的變調現象予以充分的說明。針對於變讀的情形，本文以並存音韻理論(Cophonology Theory)來作解釋，藉由*IP和ALIGN-R (Non-adjunct XP, IP)兩個制約的重新排序，得到變調與不變調兩種讀法的範疇的劃分。 / This thesis is aimed at analyzing Yinping tone sandhi in Meinong Hakka from the perspective of Optimality Theory. The discussion is divided into two parts. First, this thesis explores the tonal domain in terms of the interface of syntax and phonology. The analysis indicates that the tonal domain is founded on an intonational phrase. The formation of an intonational phrase is based on the Sense Unit Condition (Selkirk, 1984) and is closely related to restructuring (Nespor and Vogel, 1986). The special constructions of IPs are also investigated. The data supports the hypothesis proposed by Nespor and Vogel (1986), namely, that these special constructions have the privilege to form an isolated intonational phrase. Secondly, Optimality Theory is adopted to analyze the data after exploring the tonal domain. Two set of constraints are proposed in this thesis. One is that of tonal constraints, which are mainly concerned with the processing of tone sandhi. The other is that of prosodic constraints, which are responsible for explaining the delimitation of the tonal domains of the data. The two sets of constraints can be used to account for the operation of the sandhi phenomena in ordinary sentences and also in special constructions. The alternative readings are explained by means of the re-ranking of *IP and ALIGN-R (Non-adjunct XP, IP) from the perspective of Cophonology Theory.

本論文以優選理論探討上海話之入聲變調，試圖將文獻中所認為表現不規律之入聲變調納入與舒聲變調相容之分析中。本研究認為入聲變調與舒聲變調皆受制於ANCHOR-L(tσ1, Hd)，因此其首音節之基底聲調在輸出值中皆出現於重讀音節。以此觀之，則入聲變調與舒聲變調的差異主要在於節律重音的位置：在舒聲變調中首音節重讀；在入聲變調中重音則後移──在陰入變調中係移至第二音節，在陽入變調中則移至末音節。 本論文提出兩點假設：上海話中舒聲音節為重量音節，入聲音節為輕量音節；節律結構基本上為一位於左端之雙音節音步。據此，本研究提出COINCIDE (LightHd, FT-final)，認為陰入變調中重音所以後移至第二音節是因為重讀之輕量音節傾向於由音步末音節核可(licensing)。另一方面，由於陽入的單字調為曲拱調，與陰入的水平調有別，是以本研究另外提出COINCIDE(Contour, PrWd-final)，此制約顯示陽入變調中重音的遠距移位是為了遵行「曲拱調須由末音節核可」之普遍現象。 綜述之，本論文提供了一個重量音節、節律重音、曲拱調以及邊際位置等韻律顯著位置間彼此對映的實例。此外，本研究亦顯示上海話的連讀變調涉及聲調與重音的互動，是以所提出之分析或許對相關類型之研究亦有所貢獻。 / This thesis offers an Optimality-theory approach to the tone sandhi of checked tones (TSC) in Shanghai, in an attempt to regulate its surface patterns which have long been considered anomaly as opposed to the tone sandhi of smooth tones (TSS). With a reanalysis in the present study, TSC and TSS arguably have in common that their process of tone mapping is both subject to ANCHOR-L(tσ1, Hd), by which the un- derlying tone of the initial syllable ends up at the stressed syllable in the output. It follows that TSC is different from TSS in the way that metrical head is assigned: all domains undergoing TSS are stressed on their initial syllable; only in domains of TSC does the stress move rightwards, either to the second place in the tone sandhi of Yinru (TSYI), or to the final syllable in the tone sandhi of Yangru (TSYA). Given the assumption that checked syllables and smooth syllables in Shanghai are light and heavy, respectively, in terms of moraicity, and that foot-parsing is binary and left-aligned in general, the one-syllable shift of stress in TSYI can be accounted for by positing COINCIDE(LightHd, FT-final), which sets up the preference for light stress- bearing syllables to be licensed foot-finally. On the other hand, given that Yangru in the citation forms represents a rising contour, different from the level tone of Yinru, a licensing constraint, namely COINCIDE(Contour, PrWd-final), is further posited so that the long-distance movement of metrical head observed in TSYA emerges to satisfy the requirement for the retained rising contour to be licensed word-finally. Taken together, this thesis instantiates a remarkable case of the mapping among multiple prominent positions, including heavy syllables, metrical head, contour tones, and edge positions. Also, the present analysis demonstrates that Shanghai tone sandhi involves an interaction between tone and stress, thus a contribution to the general OT tone-prominence typology literature (cf. Zhang 2001, Barnes 2002, De Lacy 2002).

Treatment planning for radiation therapy inherently involves tradeoffs, such as between tumor control and normal tissue sparing, between time-efficiency and dose quality, and between nominal plan quality and robustness. The purpose of this thesis is to develop methods that can facilitate decision making related to such tradeoffs. The main focus of the thesis is on multicriteria optimization methods where a representative set of treatment plans are first calculated and the most appropriate plan contained in this representation then selected by the treatment planner through continuous interpolation between the precalculated alternatives. These alternatives constitute a subset of the set of Pareto optimal plans, meaning plans such that no criterion can be improved without a sacrifice in another. Approximation of Pareto optimal sets is first studied with respect to fluence map optimization for intensity-modulated radiation therapy. The approximation error of a discrete representation is minimized by calculation of points one at the time at the location where the distance between an inner and outer approximation of the Pareto set currently attains its maximum. A technique for calculating this distance that is orders of magnitude more efficient than the best previous method is presented. A generalization to distributed computational environments is also proposed. Approximation of Pareto optimal sets is also considered with respect to direct machine parameter optimization. Optimization of this form is used to calculate representations where any interpolated treatment plan is directly deliverable. The fact that finite representations of Pareto optimal sets have approximation errors with respect to Pareto optimality is addressed by a technique that removes these errors by a projection onto the exact Pareto set. Projections are also studied subject to constraints that prevent the dose-volume histogram from deteriorating. Multicriteria optimization is extended to treatment planning for volumetric-modulated arc therapy and intensity-modulated proton therapy. Proton therapy plans that are robust against geometric errors are calculated by optimization of the worst case outcome. The theory for multicriteria optimization is extended to accommodate this formulation. Worst case optimization is shown to be preferable to a previous more conservative method that also protects against uncertainties which cannot be realized in practice. / En viktig aspekt av planering av strålterapibehandlingar är avvägningar mellan behandlingsmål vilka står i konflikt med varandra. Exempel på sådana avvägningar är mellan tumörkontroll och dos till omkringliggande frisk vävnad, mellan behandlingstid och doskvalitet, och mellan nominell plankvalitet och robusthet med avseende på geometriska fel. Denna avhandling syftar till att utveckla metoder som kan underlätta beslutsfattande kring motstridiga behandlingsmål. Primärt studeras en metod för flermålsoptimering där behandlingsplanen väljs genom kontinuerlig interpolation över ett representativt urval av förberäknade alternativ. De förberäknade behandlingsplanerna utgör en delmängd av de Paretooptimala planerna, det vill säga de planer sådana att en förbättring enligt ett kriterium inte kan ske annat än genom en försämring enligt ett annat. Beräkning av en approximativ representation av mängden av Paretooptimala planer studeras först med avseende på fluensoptimering för intensitetsmodulerad strålterapi. Felet för den approximativa representationen minimeras genom att innesluta mängden av Paretooptimala planer mellan inre och yttre approximationer. Dessa approximationer förfinas iterativt genom att varje ny plan genereras där avståndet mellan approximationerna för tillfället är som störst. En teknik för att beräkna det maximala avståndet mellan approximationerna föreslås vilken är flera storleksordningar snabbare än den bästa tidigare kända metoden. En generalisering till distribuerade beräkningsmiljöer föreslås även. Approximation av mängden av Paretooptimala planer studeras även för direkt maskinparameteroptimering, som används för att beräkna representationer där varje interpolerad behandlingsplan är direkt levererbar. Det faktum att en ändlig representation av mängden av Paretooptimala lösningar har ett approximationsfel till Paretooptimalitet hanteras via en metod där en interpolerad behandlingsplan projiceras på Paretomängden. Projektioner studeras även under bivillkor som förhindrar att den interpolerade planens dos-volym histogram kan försämras. Flermålsoptimering utökas till planering av rotationsterapi och intensitetsmodulerad protonterapi. Protonplaner som är robusta mot geometriska fel beräknas genom optimering med avseende på det värsta möjliga utfallet av de föreliggande osäkerheterna. Flermålsoptimering utökas även teoretiskt till att innefatta denna formulering. Nyttan av värsta fallet-optimering jämfört med tidigare mer konservativa metoder som även skyddar mot osäkerheter som inte kan realiseras i praktiken demonstreras experimentellt. / <p>QC 20130527</p>

We have considered the bilevel programming problem in the case where the lower-level problem admits more than one optimal solution. It is well-known in the literature that in such a situation, the problem is ill-posed from the view point of scalar objective optimization. Thus the optimistic and pessimistic approaches have been suggested earlier in the literature to deal with it in this case. In the thesis, we have developed a unified approach to derive necessary optimality conditions for both the optimistic and pessimistic bilevel programs, which is based on advanced tools from variational analysis. We have obtained various constraint qualifications and stationarity conditions depending on some constructive representations of the solution set-valued mapping of the follower’s problem. In the auxiliary developments, we have provided rules for the generalized differentiation and robust Lipschitzian properties for the lower-level solution setvalued map, which are of a fundamental interest for other areas of nonlinear and nonsmooth optimization. Some of the results of the aforementioned theory have then been applied to derive stationarity conditions for some well-known transportation problems having the bilevel structure.

In interference-limited wireless networks, interference management techniques are important in order to improve the performance of the systems. Given that spectrum and energy are scarce resources in these networks, techniques that exploit the resources efficiently are desired. We consider a set of base stations operating concurrently in the same spectral band. Each base station is equipped with multiple antennas and transmits data to a single-antenna mobile user. This setting corresponds to the multiple-input single-output (MISO) interference channel (IFC). The receivers are assumed to treat interference signals as noise. Moreover, each transmitter is assumed to know the channels between itself and all receivers perfectly. We study the conflict between the transmitter-receiver pairs (links) using models from game theory and microeconomic theory. These models provide solutions to resource allocation problems which in our case correspond to the joint beamforming design at the transmitters. Our interest lies in solutions that are Pareto optimal. Pareto optimality ensures that it is not further possible to improve the performance of any link without reducing the performance of another link. Strategic games in game theory determine the noncooperative choice of strategies of the players. The outcome of a strategic game is a Nash equilibrium. While the Nash equilibrium in the MISO IFC is generally not efficient, we characterize the necessary null-shaping constraints on the strategy space of each transmitter such that the Nash equilibrium outcome is Pareto optimal. An arbitrator is involved in this setting which dictates the constraints at each transmitter. In contrast to strategic games, coalitional games provide cooperative solutions between the players. We study cooperation between the links via coalitional games without transferable utility. Cooperative beamforming schemes considered are either zero forcing transmission or Wiener filter precoding. We characterize the necessary and sufficient conditions under which the core of the coalitional game with zero forcing transmission is not empty. The core solution concept specifies the strategies with which all players have the incentive to cooperate jointly in a grand coalition. While the core only considers the formation of the grand coalition, coalition formation games study coalition dynamics. We utilize a coalition formation algorithm, called merge-and-split, to determine stable link grouping. Numerical results show that while in the low signal-to-noise ratio (SNR) regime noncooperation between the links is efficient, at high SNR all links benefit in forming a grand coalition. Coalition formation shows its significance in the mid SNR regime where subset link cooperation provides joint performance gains. We use the models of exchange and competitive market from microeconomic theory to determine Pareto optimal equilibria in the two-user MISO IFC. In the exchange model, the links are represented as consumers that can trade goods within themselves. The goods in our setting correspond to the parameters of the beamforming vectors necessary to achieve all Pareto optimal points in the utility region. We utilize the conflict representation of the consumers in the Edgeworth box, a graphical tool that depicts the allocation of the goods for the two consumers, to provide closed-form solution to all Pareto optimal outcomes. The exchange equilibria are a subset of the points on the Pareto boundary at which both consumers achieve larger utility then at the Nash equilibrium. We propose a decentralized bargaining process between the consumers which starts at the Nash equilibrium and ends at an outcome arbitrarily close to an exchange equilibrium. The design of the bargaining process relies on a systematic study of the allocations in the Edgeworth box. In comparison to the exchange model, a competitive market additionally defines prices for the goods. The equilibrium in this economy is called Walrasian and corresponds to the prices that equate the demand to the supply of goods. We calculate the unique Walrasian equilibrium and propose a coordination process that is realized by the arbitrator which distributes the Walrasian prices to the consumers. The consumers then calculate in a decentralized manner their optimal demand corresponding to beamforming vectors that achieve the Walrasian equilibrium. This outcome is Pareto optimal and lies in the set of exchange equilibria. In this thesis, based on the game theoretic and microeconomic models, efficient beamforming strategies are proposed that jointly improve the performance of the systems. The gained results are applicable in interference-limited wireless networks requiring either coordination from the arbitrator or direct cooperation between the transmitters.