yes / This paper discusses Leibniz’s view and defence of heliocentrism, which was one of the main achievements of the Scientific Revolution (1543-1687). As Leibniz was a defender of a strictly mechanistic worldview, it seems natural to assume that he accepted Copernican heliocentrism and its completion by figures like Kepler, Descartes and Newton without reservation. However, the fact that Leibniz speaks of the Copernican theory as a hypothesis (or plausible assumption) suggests that he had several reservations regarding heliocentrism. On a first approach Leibniz employed two of his most cherished principles to defend the Copernican hypothesis against the proponents of geocentrism: these were the principle of the relativity of motion and the principle of the equivalence of hypotheses. A closer analysis reveals, however, that Leibniz also appeals to dynamic causes of planetary motions, and these constitute a much stronger support for heliocentrism than his two philosophical principles alone.

Verification is an important step for Integrated Circuit (IC) design. In fact, literature has reported that up to 70% of the design effort is spent on checking if the design is functionally correct. One of the core verification tasks is Equivalence Checking (EC), which attempts to check if two structurally different designs are functionally equivalent for all reachable states. Powerful equivalence checking can also provide opportunities for more aggressive logic optimizations, meeting different goals such as smaller area, better performance, etc. The success of Combinational Equivalence Checking (CEC) has laid a foundation to industry-level combinational logic synthesis and optimization. However, Sequential Equivalence Checking (SEC) still faces much challenge, especially for those complex circuits that have different state encodings and few internal signal equivalences. In this thesis, we propose a novel simulation-based multi-node inductive invariant generation and pruning technique to check the equivalence of sequential circuits that have different state encodings and very few equivalent signals between them. By first grouping flip-flops into smaller subsets to make it scalable for large designs, we then propose a constrained logic synthesis technique to prune potential multi-node invariants without inadvertently losing important constraints. Our pruning technique guarantees the same conclusion for different instances (proving SEC or not) compared to previous approaches in which merging of such potential invariants might lose important relations if the merged relation does not turn out to be a true invariant. Experimental results show that the smaller invariant set can be very effective for sequential equivalence checking of such hard SEC instances. Our approach is up to 20x-- faster compared to previous mining-based methods for larger circuits. / Master of Science

Current interest in cover cropping is focused on enhancing ecosystem services beyond soil conservation. Cover crop (CC) species function uniquely in their effects on ecosystem services when grown in monoculture or mixtures. This research integrated field experiments and a literature synthesis to evaluate the role of cover crops in improving nitrogen (N) management and simultaneously providing multiple ecosystem services. Legume CC fertilized with poultry litter (PL) could replace 101 to 117 kg N ha-1 of fertilizer in corn (Zea mays L.) production. Rye (Secale cereale L.) CC fertilized with PL had a negligible effect on corn production. Biculture fertilizer equivalence ranged between -12 to +75 kg N ha-1. Fertilizer equivalence of legume-containing treatments increased across time. Without CC, fall-applied PL failed to supply N to corn. Ecosystem services of CC and PL illustrate complex species functions. Bicultures produced more total biomass than monocultures in year 1 but less than rye in year 2. Bicultures were as effective in suppressing weeds as rye, produced corn yield similar to legume, and by the second year had similar amounts of available soil N as the legume. Poultry litter effects and interspecific effects cover crop species biomass differed. Rye yield increased, while legume yield decreased slightly in biculture. Poultry litter increased legume N content and a decrease in legume C:N, while rye N content and C:N were unaffected. The synthesis corroborates that mixed and biculture cover crops yield more than the individual component species. Overyielding was transgressive in 60% of cases studied. Mixture effects varied by species: rye and brassica yield increased, while legume decreased in mixtures. The effect of mixed CC on crop yields varied by crop species and management practices, though generally crops increased 8 to 18% overall. This work can be applied to the design of complex CC and PL systems that optimize individual species functions to enhance ecosystem services. / Ph. D. / Current interest in cover cropping is focused on enhancing ecosystem services beyond soil conservation. Cover crop (CC) species function uniquely in their effects on ecosystem services when grown in monoculture or mixtures. This research integrated field experiments and a literature synthesis to evaluate the role of cover crops in improving nitrogen (N) management and simultaneously providing multiple ecosystem services. Legume CC fertilized with poultry litter (PL) could replace almost half of the inorganic fertilizer required by spring corn (<i>Zea mays</i> L.) production. Rye (<i>Secale cereale</i> L.) CC fertilized with PL had a negligible effect on corn production. Fertilizer equivalence of legume-containing treatments increased across time. Without CC, fall-applied PL failed to supply N to corn. Bicultures produced more total biomass than monocultures in year 1 but less than rye in year 2. Bicultures were as effective in suppressing weeds as rye, produced corn yield similar to legume, and by the second year had similar amounts of available soil N as the legume. Poultry litter effects and interspecific effects cover crop species biomass differed as well. Rye yield increased, while legume yield decreased slightly in biculture. Poultry litter increased legume N content and a decrease in legume C:N, while rye N content and C:N were unaffected. The synthesis corroborates that mixed and biculture cover crops yield more than the individual component species. Mixture effects varied by species: rye and brassica yield increased, while legume decreased in mixtures. The effect of mixed CC on crop yields varied by crop species and management practices, though generally crops increased 8 to 18% overall. This work can be applied to the design of complex CC and PL systems that optimize individual species functions to enhance ecosystem services.

A conditional discrimination training procedure was used to establish stimulus-stimulus relations that might lead to the emergence of relations that define playing by ear. The participants were four college students. Overall, the results varied across participants. Of the 3 participants who received Training 1 (hear-note-name/select-key), all 3 participants acquired that relation. Out of those 3 participants, 2 participants showed emergence of the hear-see-key-pressed/say-note-name relation after Training 1. Of the 3 participants who received Training 2, (hear-note-name/select-tone), 2 participants acquired that relation for at least one set. Out of those 3 participants, 1 participant showed emergence of the hear-tone/say-note-name relation. One out of three participants was successful in correctly playing a sequence of four notes by ear at the end of the study. One participant did not complete the study due to availability conflicts. The overall results can suggest that the relations used in this study should be taken into account when training someone to play by ear. However, the current data do not allow us to conclude whether it is necessary to teach or test all of these relations in order to teach playing by ear.

Participants demonstrate the Stroop effect when, in naming the color in which a word appears, reaction times are longer when the color and word are incongruent (e.g., "yellow" printed in blue) compared to when they are congruent (e.g., "yellow" printed in yellow). The literature commonly refers to the difference in reaction times as a measure of the interference of word stimuli upon color stimuli, and is taken as support for the theory of automaticity. This study asks whether the Stroop effect can be analyzed as interactions within and across stimulus classes. Adult participants learned three 3-member classes (color, word, and pattern) in a serialized order of training. In the testing phase, participants were presented with compound stimuli formed from combinations of members within and across classes (e.g., word and color), and reaction times were recorded in similar fashion to the Stroop task. Results show that averaged participants' reaction times are faster to compound stimuli comprised of members within the same class, compared to compound stimuli formed with members from different classes. These group-level data are consistent with the Stroop literature in that congruent compounds produce faster reaction times relative to incongruent compounds. However, individual participant data do not consistently reflect the Stroop effect. Further considerations for future research in this area are discussed.

In this paper we explore coloring theorems for the reals, its quotients, cardinals, and their combinations. This work is done under the scope of the axiom of determinacy. We also explore generalizations of Mycielski's theorem and show how these can be used to establish coloring theorems. To finish, we discuss the strange realm of long unions.

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.

Les nouvelles technologies jouent un rôle croissant dans notre société. Le droit s’est interrogé sur la façon de rendre possible l’utilisation du support électronique dans un monde où seule l’utilisation du support papier était possible jusqu’à peu. L’objectif était d’éviter que la loi par son attachement au support papier n’entrave l’utilisation des nouvelles technologies et plus largement le développement des échanges en ligne. Dans ce contexte, la Commission des Nations Unies pour le Développement du Commerce International (CNUDCI) a développé les principes de neutralité technologique et d’équivalence fonctionnelle aux termes desquels les écrits électroniques sont considérés comme équivalents à ceux papiers s’ils sont en mesure d’endosser les mêmes fonctions que ces derniers. Le législateur français, s’inspirant des travaux de la CNUDCI, a modifié sa législation pour permettre la reconnaissance de la valeur juridique des actes passés par voie électronique. La reconnaissance de la valeur juridique des actes conclus par voie électronique laisse cependant subsister certaines questions relatives la protection du consentement de celui qui contracte en ligne. Le législateur français a ainsi élaboré des règles formalistes et dérogatoires au droit commun concernant la conclusion des contrats électroniques pour protéger le consommateur en ligne. / New technologies play a growing role in the modern world. Some concerns have therefore been raised to determine how to enable the legal use of electronic paper where until recently, only paper support had existed. The main role of such concerns was to avoid that the existing regulations might prejudice development of new technologies (and in a broader way, of online exchange) because only paper support was taken into account. In this context, the United Nations Commission on International Trade Law (UNCITRAL) has developed the principles of technological neutrality and functional equivalence. Pursuant to those principles, electronic writing is considered as equivalent to paper writing as long as the same functions are maintained. The French legislator has sought inspiration in the works of the UNCITRAL to modify the French regulations regarding electronic support. Despite this recognition, some issues remain pending, especially regarding protection of the consent for the online contractor. In this respect, the French legislator has established formalist rules and rules that constitute exception to ordinary law.

Les nouvelles technologies jouent un rôle croissant dans notre société. Le droit s’est interrogé sur la façon de rendre possible l’utilisation du support électronique dans un monde où seule l’utilisation du support papier était possible jusqu’à peu. L’objectif était d’éviter que la loi par son attachement au support papier n’entrave l’utilisation des nouvelles technologies et plus largement le développement des échanges en ligne. Dans ce contexte, la Commission des Nations Unies pour le Développement du Commerce International (CNUDCI) a développé les principes de neutralité technologique et d’équivalence fonctionnelle aux termes desquels les écrits électroniques sont considérés comme équivalents à ceux papiers s’ils sont en mesure d’endosser les mêmes fonctions que ces derniers. Le législateur français, s’inspirant des travaux de la CNUDCI, a modifié sa législation pour permettre la reconnaissance de la valeur juridique des actes passés par voie électronique. La reconnaissance de la valeur juridique des actes conclus par voie électronique laisse cependant subsister certaines questions relatives la protection du consentement de celui qui contracte en ligne. Le législateur français a ainsi élaboré des règles formalistes et dérogatoires au droit commun concernant la conclusion des contrats électroniques pour protéger le consommateur en ligne. / New technologies play a growing role in the modern world. Some concerns have therefore been raised to determine how to enable the legal use of electronic paper where until recently, only paper support had existed. The main role of such concerns was to avoid that the existing regulations might prejudice development of new technologies (and in a broader way, of online exchange) because only paper support was taken into account. In this context, the United Nations Commission on International Trade Law (UNCITRAL) has developed the principles of technological neutrality and functional equivalence. Pursuant to those principles, electronic writing is considered as equivalent to paper writing as long as the same functions are maintained. The French legislator has sought inspiration in the works of the UNCITRAL to modify the French regulations regarding electronic support. Despite this recognition, some issues remain pending, especially regarding protection of the consent for the online contractor. In this respect, the French legislator has established formalist rules and rules that constitute exception to ordinary law.

Ma thèse se situe à l'intersection de \textit {la théorie des groupes géométrique} et \textit{la théorie des groupes mesurée}. Une question majeure dans la théorie des groupes géométrique est d'étudier la classe de quasi-isométrie (QI) et la classe d'équivalence mesurée (ME) d'un groupe, respectivement. $L^p$-équivalence mesurée est une relation d'équivalence qui est définie en ajoutant des contraintes géométriques avec d'équivalence mesurée. En plus, QI est une condition géométrique. Il est une question naturelle, si deux groupes sont QI et ME, si elles sont $L^p$-ME pour certains $p>0$. Dans mon premier article, en collaboration avec R. Tessera, nous répondons négativement à cette question pour $p\geq 1$, montrant que l'extension centrale canonique d'un groupe surface de genre plus élevé ne sont pas $L^1$-ME pour le produit direct de ce groupe de surface avec $\mathbb{Z}$ (alors qu'ils sont à la fois quasi-isométrique et équivalente mesurée).Dans mon deuxième papier, j'ai observé un lien général entre la géométrie des expandeurs, defini comme une séquence des quotients finis ( l'espace de boîte) d'un groupe finiment engendré, et les propriétés mesurée theorique du groupe. Plus précisément, je l'ai prouvé que si deux <<espaces de boîte>> sont quasi-isométrique, les groupes correspondants doivent être <<mesurée équivalente uniformément >>, une notion qui combine à la fois QI et ME. Je prouve aussi une version de ce résultat pour le plongement grossière, ce qui permet de distinguer plusieurs classe des expandeurs. Par exemple, je montre que les expandeurs associé à $SL(m, \mathbb{Z})$ ne grossièrement plongent à les expandeurs associés à $SL_n(\mathbb{Z})$ si $m>n$. / My thesis lies at the intersection of \textit{geometric group theory} and \textit{measured group theory}. A major question in geometric group theory is to study the quasi-isometry (QI) class and the measure equivalence (ME) class of a group, respectively. $L^p$-measure equivalence is an equivalence relation which is defined by adding some geometric constraints with measure equivalence. Besides, quasi-isometry is a geometric condition. It is a natural question if two groups are QI and ME, whether they are $L^p$-ME for some $p>0$. In my first paper, together with R. Tessera, we answer this question negatively for $p\geq 1$, showing that the canonical central extension of a surface group of higher genus is not $L^1$-ME to the direct product of this surface group with $\mathbb{Z}$ (while they are both quasi-isometric and measure equivalent). In my second paper, I observed a general link between the geometry of expanders arising as a sequence of finite quotients (box space) of a finitely generated group, and the measured theoretic properties of the group. More precisely, I proved that if two box spaces' are quasi-isometric, then the corresponding groups must be `uniformly measure equivalent', a notion that combines both quasi-isometry and measure equivalence. I also prove a version of this result for coarse embedding, allowing to distinguish many classes of expanders. For instance, I show that the expanders associated to $SL(m,\mathbb{Z})$ do not coarsely embed inside the expanders associated to $SL_n(\mathbb{Z}$ if $m>n$.