Aspects of Integrability in Gauge/String Correspondence

In this thesis, we present our work about some generalisations of ideas, techniques and physical interpretations typical for integrable models to one of the most outstanding advances in theoretical physics of nowadays: the AdS/CFT correspondences. We have undertaken the problem of testing this conjectured duality under various points of view, but with a clear starting point - the integrability - and with a clear ambitious task in mind: to study the finite-size effects in the energy spectrum of certain string solutions on a side and in the anomalous dimensions of the gauge theory on the other. Of course, the final desire woul be the exact comparison between these two faces of the gauge/string duality. In few words, the original part of this work consists in application of well known integrability technologies, in large parte borrowed by the study of relativistic (1+1)-dimensional integrable quantum field theories, to the highly non-relativisic and much complicated case of the thoeries involved in the recent conjectures of AdS5/CFT4 and AdS4/CFT3 corrspondences. In details, exploiting the spin chain nature of the dilatation operator of N = 4 Super-Yang-Mills theory, we concentrated our attention on one of the most important sector, namely the SL(2) sector - which is also very intersting for the QCD understanding - by formulating a new type of nonlinear integral equation (NLIE) based on a previously guessed asymptotic Bethe Ansatz. The solutions of this Bethe Ansatz are characterised by the length L of the correspondent spin chain and by the number s of its excitations. A NLIE allows one, at least in principle, to make analytical and numerical calculations for arbitrary values of these parameters. The results have been rather exciting. In the important regime of high Lorentz spin, the NLIE clarifies how it reduces to a linear integral equations which governs the subleading order in s, o(s0). This also holds in the regime with L ! 1, L/ ln s finite (long operators case). This region of parameters has been particularly investigated in literature especially because of an intriguing limit into the O(6) sigma model defined on the string side. One of the most powerful methods to keep under control the finite-size spectrum of an integrable relativistic theory is the so called thermodynamic Bethe Ansatz (TBA). We proposed a highly non-trivial generalisation of this technique to the non-relativistic case of AdS5/CFT4 and made the first steps in order to determine its full spectrum - of energies for the AdS side, of anomalous dimensions for the CFT one - at any values of the coupling constant and of the size. At the leading order in the size parameter, the calculation of the finite-size corrections is much simpler and does not necessitate the TBA. It consists in deriving for a nonrelativistc case a method, invented for the first time by L¨uscher to compute the finite-size effects on the mass spectrum of relativisic theories. So, we have formulated a new version of this approach to adapt it to the case of recently found classical string solutions on AdS4 × CP3, inside the new conjecture of an AdS4/CFT3 correspondence. Our results in part confirm the string and algebraic curve calculations, in part are completely new and then could be better understood by the rapidly evolving developments of this extremely exciting research field.

Performance evaluation of low environmental impact asphalt concretes using the mechanistic empirical design method based on laboratory fatigue and permanent deformation models

The "sustainability" concept relates to the prolonging of human economic systems with as little detrimental impact on ecological systems as possible. Construction that exhibits good environmental stewardship and practices that conserve resources in a manner that allow growth and development to be sustained for the long-term without degrading the environment are indispensable in a developed society. Past, current and future advancements in asphalt as an environmentally sustainable paving material are especially important because the quantities of asphalt used annually in Europe as well as in the U.S. are large. The asphalt industry is still developing technological improvements that will reduce the environmental impact without affecting the final mechanical performance. Warm mix asphalt (WMA) is a type of asphalt mix requiring lower production temperatures compared to hot mix asphalt (HMA), while aiming to maintain the desired post construction properties of traditional HMA. Lowering the production temperature reduce the fuel usage and the production of emissions therefore and that improve conditions for workers and supports the sustainable development. Even the crumb-rubber modifier (CRM), with shredded automobile tires and used in the United States since the mid 1980s, has proven to be an environmentally friendly alternative to conventional asphalt pavement. Furthermore, the use of waste tires is not only relevant in an environmental aspect but also for the engineering properties of asphalt [Pennisi E., 1992]. This research project is aimed to demonstrate the dual value of these Asphalt Mixes in regards to the environmental and mechanical performance and to suggest a low environmental impact design procedure. In fact, the use of eco-friendly materials is the first phase towards an eco-compatible design but it cannot be the only step. The eco-compatible approach should be extended also to the design method and material characterization because only with these phases is it possible to exploit the maximum potential properties of the used materials. Appropriate asphalt concrete characterization is essential and vital for realistic performance prediction of asphalt concrete pavements. Volumetric (Mix design) and mechanical (Permanent deformation and Fatigue performance) properties are important factors to consider. Moreover, an advanced and efficient design method is necessary in order to correctly use the material. A design method such as a Mechanistic-Empirical approach, consisting of a structural model capable of predicting the state of stresses and strains within the pavement structure under the different traffic and environmental conditions, was the application of choice. In particular this study focus on the CalME and its Incremental-Recursive (I-R) procedure, based on damage models for fatigue and permanent shear strain related to the surface cracking and to the rutting respectively. It works in increments of time and, using the output from one increment, recursively, as input to the next increment, predicts the pavement conditions in terms of layer moduli, fatigue cracking, rutting and roughness. This software procedure was adopted in order to verify the mechanical properties of the study mixes and the reciprocal relationship between surface layer and pavement structure in terms of fatigue and permanent deformation with defined traffic and environmental conditions. The asphalt mixes studied were used in a pavement structure as surface layer of 60 mm thickness. The performance of the pavement was compared to the performance of the same pavement structure where different kinds of asphalt concrete were used as surface layer. In comparison to a conventional asphalt concrete, three eco-friendly materials, two warm mix asphalt and a rubberized asphalt concrete, were analyzed. The First Two Chapters summarize the necessary steps aimed to satisfy the sustainable pavement design procedure. In Chapter I the problem of asphalt pavement eco-compatible design was introduced. The low environmental impact materials such as the Warm Mix Asphalt and the Rubberized Asphalt Concrete were described in detail. In addition the value of a rational asphalt pavement design method was discussed. Chapter II underlines the importance of a deep laboratory characterization based on appropriate materials selection and performance evaluation. In Chapter III, CalME is introduced trough a specific explanation of the different equipped design approaches and specifically explaining the I-R procedure. In Chapter IV, the experimental program is presented with a explanation of test laboratory devices adopted. The Fatigue and Rutting performances of the study mixes are shown respectively in Chapter V and VI. Through these laboratory test data the CalME I-R models parameters for Master Curve, fatigue damage and permanent shear strain were evaluated. Lastly, in Chapter VII, the results of the asphalt pavement structures simulations with different surface layers were reported. For each pavement structure, the total surface cracking, the total rutting, the fatigue damage and the rutting depth in each bound layer were analyzed.

Generalized Differential Quadrature Finite Element Method applied to Advanced Structural Mechanics

Over the years the Differential Quadrature (DQ) method has distinguished because of its high accuracy, straightforward implementation and general ap- plication to a variety of problems. There has been an increase in this topic by several researchers who experienced significant development in the last years. DQ is essentially a generalization of the popular Gaussian Quadrature (GQ) used for numerical integration functions. GQ approximates a finite in- tegral as a weighted sum of integrand values at selected points in a problem domain whereas DQ approximate the derivatives of a smooth function at a point as a weighted sum of function values at selected nodes. A direct appli- cation of this elegant methodology is to solve ordinary and partial differential equations. Furthermore in recent years the DQ formulation has been gener- alized in the weighting coefficients computations to let the approach to be more flexible and accurate. As a result it has been indicated as Generalized Differential Quadrature (GDQ) method. However the applicability of GDQ in its original form is still limited. It has been proven to fail for problems with strong material discontinuities as well as problems involving singularities and irregularities. On the other hand the very well-known Finite Element (FE) method could overcome these issues because it subdivides the computational domain into a certain number of elements in which the solution is calculated. Recently, some researchers have been studying a numerical technique which could use the advantages of the GDQ method and the advantages of FE method. This methodology has got different names among each research group, it will be indicated here as Generalized Differential Quadrature Finite Element Method (GDQFEM).

A new method for the estimation of the reverberation time from measured room impulse responses with application to Italian opera houses

The Schroeder's backward integration method is the most used method to extract the decay curve of an acoustic impulse response and to calculate the reverberation time from this curve. In the literature the limits and the possible improvements of this method are widely discussed. In this work a new method is proposed for the evaluation of the energy decay curve. The new method has been implemented in a Matlab toolbox. Its performance has been tested versus the most accredited literature method. The values of EDT and reverberation time extracted from the energy decay curves calculated with both methods have been compared in terms of the values themselves and in terms of their statistical representativeness. The main case study consists of nine Italian historical theatres in which acoustical measurements were performed. The comparison of the two extraction methods has also been applied to a critical case, i.e. the structural impulse responses of some building elements. The comparison underlines that both methods return a comparable value of the T30. Decreasing the range of evaluation, they reveal increasing differences; in particular, the main differences are in the first part of the decay, where the EDT is evaluated. This is a consequence of the fact that the new method returns a “locally" defined energy decay curve, whereas the Schroeder's method accumulates energy from the tail to the beginning of the impulse response. Another characteristic of the new method for the energy decay extraction curve is its independence on the background noise estimation. Finally, a statistical analysis is performed on the T30 and EDT values calculated from the impulse responses measurements in the Italian historical theatres. The aim of this evaluation is to know whether a subset of measurements could be considered representative for a complete characterization of these opera houses.

TiMMing: developing an innovative suite of bioinformatic tools to harmonize and track the origin of copy number alterations in the evolutive history of multiple myeloma

Multiple Myeloma (MM) is a hematologic cancer with heterogeneous and complex genomic landscape, where Copy Number Alterations (CNAs) play a key role in the disease's pathogenesis and prognosis. It is of biological and clinical interest to study the temporal occurrence of early alterations, as they play a disease "driver" function by deregulating key tumor pathways. This study presents an innovative bioinformatic tools suite created for harmonizing and tracing the origin of CNAs throughout the evolutionary history of MM. To this aim, large cohorts of newly-diagnosed MM (NDMM, N=1582) and Smoldering-MM (SMM, N=282) were aggregated. The tools developed in this study enable the harmonization of CNAs as obtained from different genomic platforms in such a way that a high statistical power can be obtained. By doing so, the high numerosity of those cohorts was harnessed for the identification of novel genes characterized as "driver" (NFKB2, NOTCH2, MAX, EVI5 and MYC-ME2-enhancer), and the generation of an innovative timing model, implemented with a statistical method to introduce confidence intervals in the CNAs-calls. By applying this model on both NDMM and SMM cohorts, it was possible to identify specific CNAs (1q(CKS1B)amp, 13q(RB1)del, 11q(CCND1)amp and 14q(MAX)del) and categorize them as "early"/ "driver" events. A high level of precision was guaranteed by the narrow confidence intervals in the timing estimates. These CNAs were proposed as critical MM alterations, which play a foundational role in the evolutionary history of both SMM and NDMM. Finally, a multivariate survival model was able to identify the independent genomic alterations with the greatest effect on patients’ survival, including RB1-del, CKS1B-amp, MYC-amp, NOTCH2-amp and TRAF3-del/mut. In conclusion, the alterations that were identified as both "early-drivers” and correlated with patients’ survival were proposed as biomarkers that, if included in wider survival models, could provide a better disease stratification and an improved prognosis definition.

Identification of outcome-oriented cut-offs for copy number alterations in multiple myeloma: predictive biomarkers with improved prognostic accuracy

Aim of the present study was to develop a statistical approach to define the best cut-off Copy number alterations (CNAs) calling from genomic data provided by high throughput experiments, able to predict a specific clinical end-point (early relapse, 18 months) in the context of Multiple Myeloma (MM). 743 newly diagnosed MM patients with SNPs array-derived genomic and clinical data were included in the study. CNAs were called both by a conventional (classic, CL) and an outcome-oriented (OO) method, and Progression Free Survival (PFS) hazard ratios of CNAs called by the two approaches were compared. The OO approach successfully identified patients at higher risk of relapse and the univariate survival analysis showed stronger prognostic effects for OO-defined high-risk alterations, as compared to that defined by CL approach, statistically significant for 12 CNAs. Overall, 155/743 patients relapsed within 18 months from the therapy start. A small number of OO-defined CNAs were significantly recurrent in early-relapsed patients (ER-CNAs) - amp1q, amp2p, del2p, del12p, del17p, del19p -. Two groups of patients were identified either carrying or not ≥1 ER-CNAs (249 vs. 494, respectively), the first one with significantly shorter PFS and overall survivals (OS) (PFS HR 2.15, p<0001; OS HR 2.37, p<0.0001). The risk of relapse defined by the presence of ≥1 ER-CNAs was independent from those conferred both by R-IIS 3 (HR=1.51; p=0.01) and by low quality (< stable disease) clinical response (HR=2.59 p=0.004). Notably, the type of induction therapy was not descriptive, suggesting that ER is strongly related to patients’ baseline genomic architecture. In conclusion, the OO- approach employed allowed to define CNAs-specific dynamic clonality cut-offs, improving the CNAs calls’ accuracy to identify MM patients with the highest probability to ER. As being outcome-dependent, the OO-approach is dynamic and might be adjusted according to the selected outcome variable of interest.