Unifying notions of pasting diagrams

In this work, we relate the three main formalisms for the notion of pasting diagram in strict ω-categories: Street's parity complexes, Johnson's pasting schemes and Steiner's augmented directed complexes. We first show that parity complexes and pasting schemes do not induce free ω-categories in general, contrarily to the claims made in their respective papers, by providing a counterexample. Then, we introduce a new formalism that is a strict generalization of augmented directed complexes, and corrected versions of parity complexes and pasting schemes, which moreover satisfies the aforementioned freeness property. Finally, we show that there are no other embeddings between these four formalisms

Exact synthesis of single-qubit unitaries over Clifford-cyclotomic gate sets

We generalize an efficient exact synthesis algorithm for single-qubit unitaries over the Clifford+T gate set which was presented by Kliuchnikov, Maslov and Mosca. Their algorithm takes as input an exactly synthesizable single-qubit unitary--one which can be expressed without error as a product of Clifford and T gates--and outputs a sequence of gates which implements it. The algorithm is optimal in the sense that the length of the sequence, measured by the number of T gates, is smallest possible. In this paper, for each positive even integer $n$ we consider the "Clifford-cyclotomic" gate set consisting of the Clifford group plus a z-rotation by $\frac{\pi}{n}$. We present an efficient exact synthesis algorithm which outputs a decomposition using the minimum number of $\frac{\pi}{n}$ z-rotations. For the Clifford+T case $n=4$ the group of exactly synthesizable unitaries was shown to be equal to the group of unitaries with entries over the ring $\mathbb{Z}[e^{i\frac{\pi}{n}},1/2]$. We prove that this characterization holds for a handful of other small values of $n$ but the fraction of positive even integers for which it fails to hold is 100%.Comment: v2: published versio

Coherence of Gray Categories via Rewriting

Over the recent years, the theory of rewriting has been extended in order to provide systematic techniques to show coherence results for strict higher categories. Here, we investigate a further generalization to low-dimensional weak categories, and consider in details the first non-trivial case: presentations of tricategories. By a general result, those are equivalent to the stricter Gray categories, for which we introduce a notion of rewriting system, as well as associated tools: critical pairs, termination orders, etc. We show that a finite rewriting system admits a finite number of critical pairs and, as a variant of Newman\u27s lemma in our context, that a convergent rewriting system is coherent, meaning that two parallel 3-cells are necessarily equal. This is illustrated on rewriting systems corresponding to various well-known structures in the context of Gray categories (monoids, adjunctions, Frobenius monoids). Finally, we discuss generalizations in arbitrary dimension

Développement d’une méthode SPRi-MALDI-IMS pour la quantification et l’identification des protéines dans des empreintes de tissus biologiques

Plusieurs tests médicaux, comme celui du dépistage du cancer du sein, se basent sur l’observation de section tissulaire sous un microscope. Ces tests se basent sur l’interprétation d’un spécialiste et les résultats peuvent varier d’un expert à un autre dû la subjectivité des observations. L’utilisation d’une technique analytique offrant une quantification et une identification de cibles moléculaires dans une section tissulaire permettrait aux experts de produire des diagnostics plus objectifs et diminuerait possiblement le nombre de faux diagnostics. Les travaux présentés dans ce mémoire portent sur le développement d’une technique SPRi-MALDI-IMS permettant l’imagerie en deux dimensions de protéines contenues dans une section tissulaire. La MALDI-IMS est la technique de choix pour l’imagerie de biomolécules dans les sections tissulaires. Par contre, elle ne parvient pas à elle seule à quantifier de façon absolue le matériel adsorbé à la surface. Donc, le couplage de la MALDI-IMS avec la SPRi permet la quantification absolue de protéines en deux dimensions et crée une technique répondant aux besoins des experts médicaux. Pour ce faire, nous avons étudié, l’effet de la chimie de surface sur la nature et la quantité de matériel adsorbé à la surface du capteur. De plus, la cinétique de transfert des protéines du tissu vers le capteur a dû être optimisée afin de produire des empreintes correspondant au tissu d’origine, afin d’atteindre la gamme dynamique des instruments SPRi et MALDI-IMS. La technique résultante de ces optimisations permet d’obtenir les premières images quantitatives et qualitatives de protéines en deux dimensions d’une seule section tissulaire.Several medical tests, such as breast cancer screening, are based on the observation of tissue section under a microscope. These tests rely on the interpretation of a specialist and the results can vary due to subjectivity of these analyses. Using an analytical technique able to quantify and identify molecular targets in a tissue section would enable experts to produce more objective diagnostic and possibly reduce the number of misdiagnosis. The work presented in this thesis focuses on the development of a SPRi-MALDI-IMS technique for imaging proteins in a tissue section. MALDI-IMS is the contemporary technique of choice for biomolecule imaging in tissue sections. However, absolute quantification of material absorbed to the surface cannot be performed using MALDI-IMS. The absolute quantification of proteins in two dimensions was successfully achieved by coupling of the MALDI-IMS with SPRi. Accordingly, we investigated by studying the nature of the surface chemistry and the amount of material adsorbed on the sensor’s surface. In addition, the kinetics of the protein transfer had to be optimized to produce imprints corresponding to the transferred tissue and to reach the dynamic ranges of both SPRi and MALDI-IMS instruments. The resulting technique led to quantitative and qualitative images of proteins in two dimensions of a single tissue section. It is envisioned that SPRi-MALDI-IMS can eventually meet the needs of medical experts for pathological screening

Higher-order calculations of electron-deuteron scattering in nuclear effective theory

Motivated by recent advances in the application of effective field theory techniques to light nuclei we revisit the problem of electron-deuteron scattering in these approaches. By sidestepping problems with the description of electron-nucleon scattering data in effective field theories, we show that the effective theory expansion for deuteron physics converges well over a wide range of momentum transfers. The resultant description of the physics of the two-nucleon system is good up to virtual photon momenta of order 700 MeV.Comment: 18 pages, 7 figure

Neutron charge form factor at large q2q^2

The neutron charge form factor $G_{En}(q)$ is determined from an analysis of the deuteron quadrupole form factor $F_{C2}$ data. Recent calculations, based on a variety of different model interactions and currents, indicate that the contributions associated with the uncertain two-body operators of shorter range are relatively small for $F_{C2}$, even at large momentum transfer $q$. Hence, $G_{En}(q)$ can be extracted from $F_{C2}$ at large $q^2$ without undue systematic uncertainties from theory.Comment: 8 pages, 3 figure

Electron-deuteron scattering in a current-conserving description of relativistic bound states: formalism and impulse approximation calculations

The electromagnetic interactions of a relativistic two-body bound state are formulated in three dimensions using an equal-time (ET) formalism. This involves a systematic reduction of four-dimensional dynamics to a three-dimensional form by integrating out the time components of relative momenta. A conserved electromagnetic current is developed for the ET formalism. It is shown that consistent truncations of the electromagnetic current and the $NN$ interaction kernel may be made, order-by-order in the coupling constants, such that appropriate Ward-Takahashi identities are satisfied. A meson-exchange model of the $NN$ interaction is used to calculate deuteron vertex functions. Calculations of electromagnetic form factors for elastic scattering of electrons by deuterium are performed using an impulse-approximation current. Negative-energy components of the deuteron's vertex function and retardation effects in the meson-exchange interaction are found to have only minor effects on the deuteron form factors.Comment: 42 pages, RevTe

Meson exchange currents in electromagnetic one-nucleon emission

The role of meson exchange currents (MEC) in electron- and photon-induced one-nucleon emission processes is studied in a nonrelativistic model including correlations and final state interactions. The nuclear current is the sum of a one-body and of a two-body part. The two-body current includes pion seagull, pion-in-flight and the isobar current contributions. Numerical results are presented for the exclusive 16O(e,e'p)15N and 16O(\gamma,p)15N reactions. MEC effects are in general rather small in (e,e'p), while in (\gamma,p) they are always large and important to obtain a consistent description of (e,e'p) and (\gamma,p) data, with the same spectroscopic factors. The calculated (\gamma,p) cross sections are sensitive to short-range correlations at high values of the recoil momentum, where MEC effects are larger and overwhelm the contribution of correlations.Comment: 9 pages, 6 figure

Femtometer Toroidal Structures in Nuclei

The two-nucleon density distributions in states with isospin $T=0$, spin $S$=1 and projection $M_S$=0 and $\pm$1 are studied in $^2$H, $^{3,4}$He, $^{6,7}$Li and $^{16}$O. The equidensity surfaces for $M_S$=0 distributions are found to be toroidal in shape, while those of $M_S$=$\pm$1 have dumbbell shapes at large density. The dumbbell shapes are generated by rotating tori. The toroidal shapes indicate that the tensor correlations have near maximal strength at $r<2$ fm in all these nuclei. They provide new insights and simple explanations of the structure and electromagnetic form factors of the deuteron, the quasi-deuteron model, and the $dp$, $dd$ and $\alpha d$ $L$=2 ($D$-wave) components in $^3$He, $^4$He and $^6$Li. The toroidal distribution has a maximum-density diameter of $\sim$1 fm and a half-maximum density thickness of $\sim$0.9 fm. Many realistic models of nuclear forces predict these values, which are supported by the observed electromagnetic form factors of the deuteron, and also predicted by classical Skyrme effective Lagrangians, related to QCD in the limit of infinite colors. Due to the rather small size of this structure, it could have a revealing relation to certain aspects of QCD.Comment: 35 pages in REVTeX, 25 PostScript figure