Towards Plane Spanners of Degree 3

Let S be a finite set of points in the plane that are in convex position. We present an algorithm that constructs a plane frac{3+4 pi}{3}-spanner of S whose vertex degree is at most 3. Let Lambda be the vertex set of a finite non-uniform rectangular lattice in the plane. We present an algorithm that constructs a plane 3 sqrt{2}-spanner for Lambda whose vertex degree is at most 3. For points that are in the plane and in general position, we show how to compute plane degree-3 spanners with a linear number of Steiner points

Knee joint contact stresses : the influence of deformity and muscle activity

Studies have shown that the alignment of the knee in the coronal plane has a significant effect on the joint contact stress. However, gait analysis demonstrated that factors other than alignment contributed significantly to the outcome of corrective surgery. It was therefore hypothesized that muscle contraction can alter the stress distribution within the knee joint and that overloading can occur in the absence of a deformity. Six normal knees were harvested from different donors. The exact orientation of all muscle groups was recorded and their tendinous insertions carefully preserved. Custom built pressure transducers (6 per compartment, 0.5 mm thick, 10 mm diameter) were inserted through 2 small, posterior, capsular incisions and placed on the tibial surface and the menisci. The knees were mounted in a loading system which allowed free self-alignment of the joint under load. All muscles were replaced by wire cables instrumented with force transducer, tensioner and grip. Several alignment models (5, 10 degree varus, neutral, 5 degree valgus and 15 degree of flexion) as well as the effect of contraction of all major muscles crossing the knee joint were tested. An even pressure distribution was seen in neutral alignment. In a varus deformity the peak pressure shifted medially and laterally in valgus. Unloading of the opposite compartment was seen for deformities as small as 5 degrees. A flexion deformity produced a postero-lateral shift of the peak pressure area. Muscle contraction increased the pressure significantly in a region next to the muscle. Generally, unloading - though less significant - was seen in a region diagonally across the joint. These results suggest that muscular hyperactivity may considerable increase the contact stresses. However, muscle weakness or lack of muscular contraction may indirectly play a significant role in affecting the contact pressure distribution. If the muscle force is insufficient to counterbalance the external moment condylar lift-off occurs. This increases the angulation between femur and tibia thereby overloading the compartment where contact takes place; One can therefore conclude that abnormal gait patterns or neuromuscular control mechanisms may result in unphysiologically high contact stresses which may cause the development of unicompartmental osteoarthritis and subsequently, a deformity

Greedy routing and virtual coordinates for future networks

At the core of the Internet, routers are continuously struggling with ever-growing routing and forwarding tables. Although hardware advances do accommodate such a growth, we anticipate new requirements e.g. in data-oriented networking where each content piece has to be referenced instead of hosts, such that current approaches relying on global information will not be viable anymore, no matter the hardware progress. In this thesis, we investigate greedy routing methods that can achieve similar routing performance as today but use much less resources and which rely on local information only. To this end, we add specially crafted name spaces to the network in which virtual coordinates represent the addressable entities. Our scheme enables participating routers to make forwarding decisions using only neighbourhood information, as the overarching pseudo-geometric name space structure already organizes and incorporates "vicinity" at a global level. A first challenge to the application of greedy routing on virtual coordinates to future networks is that of "routing dead-ends" that are local minima due to the difficulty of consistent coordinates attribution. In this context, we propose a routing recovery scheme based on a multi-resolution embedding of the network in low-dimensional Euclidean spaces. The recovery is performed by routing greedily on a blurrier view of the network. The different network detail-levels are obtained though the embedding of clustering-levels of the graph. When compared with higher-dimensional embeddings of a given network, our method shows a significant diminution of routing failures for similar header and control-state sizes. A second challenge to the application of virtual coordinates and greedy routing to future networks is the support of "customer-provider" as well as "peering" relationships between participants, resulting in a differentiated services environment. Although an application of greedy routing within such a setting would combine two very common fields of today's networking literature, such a scenario has, surprisingly, not been studied so far. In this context we propose two approaches to address this scenario. In a first approach we implement a path-vector protocol similar to that of BGP on top of a greedy embedding of the network. This allows each node to build a spatial map associated with each of its neighbours indicating the accessible regions. Routing is then performed through the use of a decision-tree classifier taking the destination coordinates as input. When applied on a real-world dataset (the CAIDA 2004 AS graph) we demonstrate an up to 40% compression ratio of the routing control information at the network's core as well as a computationally efficient decision process comparable to methods such as binary trees and tries. In a second approach, we take inspiration from consensus-finding in social sciences and transform the three-dimensional distance data structure (where the third dimension encodes the service differentiation) into a two-dimensional matrix on which classical embedding tools can be used. This transformation is achieved by agreeing on a set of constraints on the inter-node distances guaranteeing an administratively-correct greedy routing. The computed distances are also enhanced to encode multipath support. We demonstrate a good greedy routing performance as well as an above 90% satisfaction of multipath constraints when relying on the non-embedded obtained distances on synthetic datasets. As various embeddings of the consensus distances do not fully exploit their multipath potential, the use of compression techniques such as transform coding to approximate the obtained distance allows for better routing performances

The role of the electron recoiling mechanism in coherent light high-order harmonics generation: from the source to the applications

2008/2009I processi di generazione di armoniche di ordine superiore (High-order Harmonic Generation o HHG) in gas inerti rappresentano, attualmente, la tecnica piu` promettente per la creazione di impulsi di luce coerente nell'estremo ultra-violetto (EUV) in una configurazione table-top. I processi HHG si basano sull'interazione non-lineare, tra impulsi laser ultra-corti, tipicamente dell'ordine della decina di femtosecondi, e atomi di gas inerti. Le caratteristiche che distinguono i processi HHG sono la loro durata temporale, che puo` essere nel dominio degli attosecondo e il fatto che l'interazione e` non perturbativa. Invece, la natura quantistica dei processi HHG implica la presenza di meccanismi di diffusione che influenzano la funzione d'onda dell'elettrone atomico coinvolto nell'interazione con il campo laser. Il ruolo della diffusione viene usualmente trascurato nella letteratura corrente, sebbene quest'ultima sia strettamente legata al controllo dell'efficienza del processo HHG e dello stato di polarizzazione dei fotoni generati. Il lavoro di tesi e` focalizzato sullo studio sperimentale e teorico/fenomenologico del ruolo dei meccanismi di diffusione, e sul loro controllo, al fine di incrementare l'efficienza e la qualita` ottica, i.e. coerenza, struttura temporale, etc., dei fotoni HHG prodotti. Gli studi e gli esperimenti condotti forniscono, in base alla nostra attuale conoscenza, la prima dimostrazione quantitativa a supporto del modello di Leweinstein. Accanto alla caratterizzazione spettrale, viene presentato uno studio accurato circa le condizioni minime necessarie a generare impulsi HHG, sempre legate al ruolo della diffusione della funzione d'onda elettronica. I risultati hanno permesso di ottenere una piu` profonda comprensione della complessa dinamica non-lineare, che sta alla base dei processi HHG. Accanto allo studio della diffusione si e` cercato di ottenere il controllo sullo stato di polarizzazione degli impulsi HHG, i quali mantengono la polarizzazione della radiazione laser utilizzata. La stessa diffusione impedisce di creare efficientemente armoniche di ordine superiore con polarizzazione ellittica (o circolare). Per risovere questo problema e` stata abbiamo sviluppato una collaborazione con il gruppo CXRO del Lawrence Berkeley National Laboratory, (Berkeley, USA), grazie al quale sono state realizzate una serie di ottiche multistrati innovative basate sul principio dell'angolo di Brewster, e disegnate appositamente per polarizzare circolarmente impulsi di luce EUV. Queste ultime sono state preliminarmente testate con successo sulla beam-line 6.3.2 del sincrotrone di Berkeley. La parte finale della tesi presenta la prima sorgente di impulsi HHG, polarizzati circolarmente utilizzando i citati multistrati. Per verificare l'efficienza e` di questi multistrati e` stato condotto un esperimento di dicroismo magnetico circolare con radiazioni EUV (EUV-MCD), unico nel sul genere, in quanto utilizza gli impulsi HHG polarizzati circolarmente per sondare il comportamento dicroico in corrispondenza delle soglie di assorbimento M di metalli ferromagnetici come Fe e Ni o delle loro leghe. Il fine ultimo e` dato dalla realizzazione di un esperimento risolto in tempo capace di utlizzare impulsi HHG circolarmente polarizzati per comprendere il processo di demagnetizzazione di sistemi ferromagnetici, sulla scala temporale del femtosecondo.XXII Ciclo198

Applications of electronic structure theory to problems in strong-field chemistry, inorganic chemistry, and nanomaterial systems

This dissertation covers research performed on applications of electronic structure theory to various fields of chemistry and is divided into eight chapters. Chapters 2 through 4 describe a series of related works which explore applications of excited state electronic structure methods to problems in strong field chemistry. Chapters 5, 6, and 7 discuss the application of electronic structure theory methods to solving problems in inorganic chemistry. Finally, Chapter 8 looks at an application of electronic structure theory to nanomaterials. Chapter 2 covers the modeling of electron dynamics of butadiene interacting with a short, intense laser pulse in the absence of ionization This chapter lays down the ground work for the following two chapters by examining the effects of basis set size and number of excited states included in the TD-CI simulation on the amount of population transferred from the ground state into the excited states by the interaction with an short, intense, non-resonant laser pulse. This chapter focuses mostly on TD-CI simulations using excited state energies and transition dipole matrices found by wavefunction based methods: TD-HF, TD-CIS, and TD-CIS(D). Chapter 3 expands on the work established in Chapter 2 by examining the excited state populations of butadiene using excitation energies and transition dipoles calculated by time-dependent density functional theory. Several DFT functionals are tested including GGA, meta-GGA, hybrid and long-range corrected functionals. The degree to which excited state energies and transition dipoles contribute to the final populations of the excited states is also examined. Chapter 4 wraps up the series by including ionization using a heuristic ionization model. This chapter examines the strong-field ionization of a series of linear polyenes of increasing length: ethylene, butadiene, hexatriene, and octatetraene. Also tested is the ionization dependence on parameters of the ionization model, basis set size, and number of states included in the simulation. Chapters 5-7 discuss collaborative works with members of the inorganic division of chemistry at Wayne State University. Chapter 5 describes a study on a chiral pentadenate ligand synthesized by the Kodanko group and the geometrical preference for a single isomer out of five possible isomers. Electronic structure theory indicates that the favored geometry is due to the chiral ligand, which prefers to be in a single conformation in metal complexes due to steric interactions. Chapter 6 covers a paddlewheel dinculear Cu(II) complex synthesized by the Winter group. This complex has the shortest Cu--Cu separation reported to date and electronic structure theory is used to explore the cause of this small separation. A simple model is proposed where the metal separation is governed by twisting of the ligand due to interligand π orbital interactions. Chapter 7 describes work done in collaboration with the Verani group, exploring the redox properties of some five-coordinate Fe(III) complexes. Chapter 8 sets out to develop an inexpensive model that can be used to optimize guest systems inside single walled nanotubes. The model takes advantage of the highly polarizable nature of nanotubes. The model is calibrated using a simple hydrogen bonded system and comparisons are made to test the reliability of the model

Similarity reasoning for local surface analysis and recognition

This thesis addresses the similarity assessment of digital shapes, contributing to the analysis of surface characteristics that are independent of the global shape but are crucial to identify a model as belonging to the same manufacture, the same origin/culture or the same typology (color, common decorations, common feature elements, compatible style elements, etc.). To face this problem, the interpretation of the local surface properties is crucial. We go beyond the retrieval of models or surface patches in a collection of models, facing the recognition of geometric patterns across digital models with different overall shape. To address this challenging problem, the use of both engineered and learning-based descriptions are investigated, building one of the first contributions towards the localization and identification of geometric patterns on digital surfaces. Finally, the recognition of patterns adds a further perspective in the exploration of (large) 3D data collections, especially in the cultural heritage domain. Our work contributes to the definition of methods able to locally characterize the geometric and colorimetric surface decorations. Moreover, we showcase our benchmarking activity carried out in recent years on the identification of geometric features and the retrieval of digital models completely characterized by geometric or colorimetric patterns

Generation and characterization of spatially structured few-photon states of light

The present doctoral dissertation discusses the results of research on the characterization of spatial structure and statistical properties of few-photon states of light generated i.a. with the use of a new source based on multimode atomic memory. The dissertation comprises nine chapters grouped into the following parts: a literature and theoretical introduction, and three main parts providing the experimental results. Part I discusses the characteristics of a scientific complementary metal-oxide semiconductor camera equipped with an image intensifier (I-sCMOS) constructed by our group. We provide theoretical models of saturation of photon-number-resolving detectors which relate qualitatively to our camera. We perform experimental tomography of the I-sCMOS camera and use its results for high-fidelity reconstruction of the original statistics of the impinging light. In Part II we present an atomic memory setup in warm rubidium vapors where the write-in and readout occur due to collective Raman scattering. The memory is able to store information about the spatial structure of light. We describe the experimental setup thoroughly, with particular attention to the filtering system. We characterize multimode Raman scattering and investigate the storage performance of the memory which is limited by diffusional decoherence. We demonstrate spatial correlations between delayed Stokes and anti-Stokes photons. Using the I-sCMOS camera together with an advanced filtering system we observe spatial correlations down to single atomic excitations per memory mode. In Part III we discuss the use of the I-sCMOS camera to observe the Hong-Ou-Mandel two-photon interference with spatial resolution. We study the influence of finite spatial distinguishability of photons on the interference results, which leads us to measurements of the local spatial structure of a single photon. We observe and examine closely the following relatively unexplored phenomena. In Part I we investigate seemingly nonclassical effects in measurements of photon counts statistics on the camera. In Part II we are the first ones to show multimode Raman scattering in atomic memories. Finally, in Part III we describe the first observation of the Hong-Ou-Mandel effect with spatial resolution which is studied further in terms of finite spatial distinguishability of the interfering photons. In this thesis, we present the following novel experimental methodology. We use a new-type of I-sCMOS camera. We implement and perform the reconstruction of photon statistics based on tomographic characterization of the detector. We also build an efficient filtering system for photons generated in atomic memory. Moreover, we create an accurate method of measuring diffusion coefficients in atomic memory. We present our own methods of spatial characterization of the properties of light. Eventually, we introduce an entirely novel method: holographic measurement of the phase structure of a single photon using i.a. a specially developed phase reconstruction algorithm. The presented results fall within the scope of contemporary research in quantum optics and have a number of possible applications, as discussed in the final remarks section.Niniejsza praca doktorska prezentuje wyniki badań poświęconych charakteryzacji struktury przestrzennej i właściwości statystyk kilkufotonowych stanów światła generowanych m.in. z użyciem nowego źródła opartego na wielomodowej pamięci atomowej. Praca składająca się z 9 rozdziałów podzielona jest na wstęp literaturowy i teoretyczny oraz trzy części zawierające merytoryczne wyniki badań. Kolejno w części I prezentujemy i charakteryzujemy skonstruowany układ kamery sCMOS ze wzmacniaczem obrazu (I-sCMOS). Przedstawiamy teoretyczne modele nasycania detektorów rozróżniających liczbę fotonów, które jakościowo odnoszą się do kamery. Przeprowadzamy eksperymentalną tomografię kamery I-sCMOS a jej wyniki wykorzystujemy do wiernej rekonstrukcji pierwotnych statystyk światła padającego na kamerę. W części II prezentujemy układ pamięci atomowej w ciepłych parach rubidu, do której zapis i odczyt odbywa się w wyniku kolektywnego rozpraszania Ramana. Pamięć jest w stanie przechować informacje na temat przestrzennej struktury światła. Dokładnie opisujemy układ doświadczalny, w szczególności pod kątem układu filtrowania. Charakteryzujemy wielomodowe rozpraszanie Ramana oraz badamy zdolność przechowywania pamięci ograniczoną dekoherencją dyfuzyjną. Demonstrujemy korelacje przestrzenne pomiędzy opóźnionymi w czasie fotonami Stokesa i anty-Stokesa. Używając kamery I-sCMOS i zaawansowanego systemu filtrowania obserwujemy korelacje przestrzenne aż do reżimu pojedynczych wzbudzeń atomowych na mod pamięci. W części III wykorzystujemy kamerę I-sCMOS do badania zjawiska interferencji dwufotonowej Hong-Ou-Mandela obserwowanego z rozdzielczością przestrzenną. Studiujemy wpływ skończonej widzialności przestrzennej na wynik interferencji, która służy nam do pomiaru lokalnej struktury przestrzennej pojedynczego fotonu. Zaobserwowaliśmy i zbadaliśmy następujące słabo zbadane zjawiska. W części I badamy pozorne efekty nieklasyczne w statystykach zliczeń fotonów zmierzonych za pomocą kamery. W części II po raz pierwszy pokazujemy wielomodowe rozpraszanie Ramana w pamięciach atomowych. Natomiast w części III prezentujemy pierwszą obserwację efektu Hong-Ou-Mandela z rozdzielczością przestrzenną, którą następnie badamy pod kątem wpływu skończonej rozróżnialności przestrzennej interferujących fotonów. Na potrzeby tej pracy zostały stworzone i opracowane następujące, nowe metodologie badawcze. Stosujemy nowego typu kamerę I-sCMOS, opracowujemy rekonstrukcje statystyk fotonów na podstawie tomograficznej charakteryzacji detektora. Konstruujemy skuteczny układ filtrowania fotonów w pamięci atomowej. Tworzymy nową dokładną metodę pomiaru współczynników dyfuzji w pamięci atomowej. Prezentujemy także własne metody charakteryzacji przestrzennej statystycznych właściwości światła. W końcu, pokazujemy zupełnie nowatorską metodę holograficznego pomiaru struktury fazy pojedynczego fotonu, wykorzystującą m.in. specjalnie stworzony algorytm rekonstrukcji fazy. Zaprezentowane wyniki wpisują się w kontekst współczesnych badań w optyce kwantowej, a także posiadają szereg potencjalnych zastosowań, przedyskutowanych w podsumowaniu pracy