Conservation laws for strings in the Abelian Sandpile Model

The Abelian Sandpile generates complex and beautiful patterns and seems to display allometry. On the plane, beyond patches, patterns periodic in both dimensions, we remark the presence of structures periodic in one dimension, that we call strings. We classify completely their constituents in terms of their principal periodic vector k, that we call momentum. We derive a simple relation between the momentum of a string and its density of particles, E, which is reminiscent of a dispersion relation, E=k^2. Strings interact: they can merge and split and within these processes momentum is conserved. We reveal the role of the modular group SL(2,Z) behind these laws.Comment: 4 pages, 4 figures in colo

Deterministic Abelian Sandpile Models and Patterns

In this thesis we want to study the ASM in connection with its capability to produce interesting patterns. it is a surprising example of model that shows the emergence of patterns but maintains the property of being analytically tractable. Then it is qualitatively different from other typical growth models --like Eden model, the diffusion limit aggregation, or the surface deposition -- indeed while in these models the growth of the patterns is confined on the surfaces and the inner structures, once formed, are frozen and do not evolve anymore, in the ASM the patterns formed grow in size but at the same time the internal structures aquire structure, as it has been noted in several papers. There have been several earlier studies of the spatial patterns in sandpile models. The first of them was by Liu et.al. The asymptotic shape of the boundaries of the patterns produced in centrally seeded sandpile model on different periodic backgrounds was discussed in a work of Dhar of 1999. Borgne et.al. obtained bounds on the rate of growth of these boundaries, and later these bounds were improved by Fey et.al. and Levine et.al. An analysis of different periodic structures found in the patterns were first carried out by Ostojic who also first noted the exact quadratic nature of the toppling function within a patch. Wilson et.al. have developed a very efficient algorithm to generate patterns for a large numbers of particles added, which allows them to generate pictures of patterns with N up to 2^26. There are other models, which are related to the Abelian Sandpile Model,e.g., the Internal Diffusion-Limited Aggregation (IDLA), Eulerian walkers (also called the rotor-router model), and the infinitely-divisible sandpile, which also show similar structure. For the IDLA, Gravner and Quastel showed that the asymptotic shape of the growth pattern is related to the classical Stefan problem in hydrodynamics, and determined the exact radius of the pattern with a single point source. Levine and Peres have studied patterns with multiple sources in these models, and proved the existence of a limit shape. Limiting shapes for the non-Abelian sandpile has recently been studied by Fey et.al. The results of our investigation toward a comprehension of the patterns emerging in the ASM are reported along the thesis. In chapter 3 we will introduce some new algebraic operators, $a^\dagger_i$ and $\Pi_i$ in addition to $a_i$, over the space of the sandpile configurations, that will be in the following basic ingredients in the creation of patterns in the sandpile. We derive some Temperley-Lieb like relations they satisfy. At the end of the chapter we show how do they are closely related to multitopplings and which consequences has that relation on the action of $\Pi_i$ on recurrent configurations. In chapter 4 we search for a closed formula to characterize the Identity configuration of the ASM. At this scope we study the ASM on the square lattice, in different geometries, and in a variant with directed edges, the F-lattice or pseudo-Manhattan lattice. Cylinders, through their extra symmetry, allow an easy characterization of the identity which is a homogeneous function. In the directed version, the pseudo-Manhattan lattice, we see a remarkable exact self-similar structure at different sizes, which results in the possibility to give a closed formula for the identity, this work has been published. In chapter 5 we reach the cardinal point of our study, here we present the theory of strings and patches. The regions of a configuration periodic in space, called patches, are the ingredients of pattern formation. In a last paper of Dhar, a condition on the shape of patch interfaces has been established, and proven at a coarse-grained level. We discuss how this result is strengthened by avoiding the coarsening, and describe the emerging fine-level structures, including linear interfaces and rigid domain walls with a residual one-dimensional translational invariance. These structures, that we shall call strings, are macroscopically extended in their periodic direction, while showing thickness in a full range of scales between the microscopic lattice spacing and the macroscopic volume size. We first explore the relations among these objects and then we present full classification of them, which leads to the construction and explanation of a Sierpinski triangular structure, which displays patterns of all the possible patches

Explicit characterization of the identity configuration in an Abelian Sandpile Model

Since the work of Creutz, identifying the group identities for the Abelian Sandpile Model (ASM) on a given lattice is a puzzling issue: on rectangular portions of Z^2 complex quasi-self-similar structures arise. We study the ASM on the square lattice, in different geometries, and a variant with directed edges. Cylinders, through their extra symmetry, allow an easy determination of the identity, which is a homogeneous function. The directed variant on square geometry shows a remarkable exact structure, asymptotically self-similar.Comment: 11 pages, 8 figure

Optimasi Portofolio Resiko Menggunakan Model Markowitz MVO Dikaitkan dengan Keterbatasan Manusia dalam Memprediksi Masa Depan dalam Perspektif Al-Qur`an

Risk portfolio on modern finance has become increasingly technical, requiring the use of sophisticated mathematical tools in both research and practice. Since companies cannot insure themselves completely against risk, as human incompetence in predicting the future precisely that written in Al-Quran surah Luqman verse 34, they have to manage it to yield an optimal portfolio. The objective here is to minimize the variance among all portfolios, or alternatively, to maximize expected return among all portfolios that has at least a certain expected return. Furthermore, this study focuses on optimizing risk portfolio so called Markowitz MVO (Mean-Variance Optimization). Some theoretical frameworks for analysis are arithmetic mean, geometric mean, variance, covariance, linear programming, and quadratic programming. Moreover, finding a minimum variance portfolio produces a convex quadratic programming, that is minimizing the objective function ðð¥with constraintsð ð 𥠥 ðandð´ð¥ = ð. The outcome of this research is the solution of optimal risk portofolio in some investments that could be finished smoothly using MATLAB R2007b software together with its graphic analysis

Search for supersymmetry in events with one lepton and multiple jets in proton-proton collisions at root s=13 TeV

Peer reviewe

Search for anomalous couplings in boosted WW/WZ -> l nu q(q)over-bar production in proton-proton collisions at root s=8TeV

Peer reviewe

The representation of the onset of the Covid-19 pandemic and the consequent lockdown in Italy: A psychosocial research by SPS, Studio di Psicosociologia of Rome

A fine febbraio 2020, in SPS4ci siamo chiesti quali fossero i vissuti evocati dalla pandemia Covid-19 in esordio, e quali fatti “derivassero” da tali vissuti. A tal fine abbiamo interpellato 419 persone, tra l’1 marzo e il 5 maggio 2020. Il corpus raccolto è stato analizzato con l’Analisi Emozionale del Testo (AET). Si ipotizzava che la pandemia avesse destrutturato le modalità abituali di rapporto, e pensavamo stessero emergendo dimensioni relazionali inedite. I nostri dati dicono che l’individualismo abituale, di avida competitività, è in crisi. In risposta alla destrutturazione dello schema relazionale amico/nemico, alla base della socialità, è emerso un nuovo individualismo. La rappresentazione del pericolo insito nel contagio pandemico ci ha reso, tutti, potenzialmente nemici gli uni degli altri. Tutti siamo vissuti come potenzialmente nemici di tutti, a meno di non essere dichiaratamente malati. I malati, di contro, non sono vissuti come nemici: sono un’alterità scissa, relegata in un altrove lontano da chi è “sano”. Le cure, nel lockdown, erano confinate nell’ospedale, caratterizzate dall’isolamento, dall’emergenza, dalla morte esperita nel peggiore dei modi. L’altrove è stato reificato in un ospedale diventato sintomatico del fallimento del sistema sanitario. Si è costituito un “noi” qui insieme, sani e maniacalmente felici, e un “loro”contagiati, dannati, isolati e “altrove”. Internet, consentendo vicinanza senza contatto, è diventata un nuovo contesto di socialità. Ha permesso di ridiventare umani, ovvero amici, a meno che non si dimostri il contrario. Ma la nuova amicalità è fondata sulla scissione dall’altro dannato: la coppia malato/curante, e tutti gli esclusi, per diverse motivazioni, dalla protezione del lockdown. Dalla nuova socialità è escluso anche il vissuto dello stare chiusi in casa con gli abituali conviventi, dove emerge la violenza delle relazioni familiari obbligate. Si evidenziano altri esclusi dal noi maniacalmente amicale: gli anziani che non usano internet e che più di tutti rischiano di morire. C’è poi una cultura che, entro il fallimento delle relazioni sociali abituali, sottolinea l’impotenza delle istituzioni (politiche, sanitarie, mediatiche etc.) nella contingenza pandemica. Infine, c’è una cultura pre-lockdown, fatta della paura che porterà a scegliere l’isolamento. Manca, nei dati, il mondo produttivo, che non ha ritrovato, per gli interpellati dalla ricerca –nel periodo di tempo da noi considerato –un codice emozionale condiviso che potesse raccogliersi in un cluster. La ricerca aveva anche un obiettivo di intervento: quello di creare un contesto in cui l’evento pandemia potesse essere interpretato, entro un setting di partecipazione. Oltre a effettuare una pubblicazione rapida dei dati, intendiamo promuovere gruppi di discussione su internet con i partecipanti. La creazione di un contesto di condivisione è anche un motivo dell’alto numero di Autori.At the end of February 2020, in SPS2we asked ourselves what were the experiences evoked by the Covid-19 pandemic in its debut, and what facts “derived”from these experiences. To this end, we interviewed 419 people, between 1 March and 5 May 2020. The collected corpus was analyzed through the Emotional Text Analysis (AET). It was assumed that the pandemic had deconstructed the usual ways of relating, and we thought that new relational dimensions were emerging. Our data show that habitual individualism, of greedy competitiveness, is in crisis. A new individualism has emerged in response to the deconstruction of the friend/foerelational schema, at the basis of sociality. The representation of the danger inherent in the pandemic contagion has made us all potentially enemies of each other. We have all lived as potentially enemies of all, unless we are admittedly sick. The sick, on the other hand, are not experienced as enemies: they are a split otherness, relegated to an elsewhere far from those who are “healthy”. Duringthe lockdown, treatments were confined to the hospital, characterized by isolation, emergency, death experienced in the worst way. The othernesswas reified in a hospital that became symptomatic of the failure of the health system. A “we”has formed here together, healthy and maniacally happy, and a “them”infected, damned, isolated and “elsewhere”. The Internet, by allowing contactless proximity, has become a new context of sociality. It has allowed us to become human again, or friends, unless proven otherwise. But the new friendship is based on the split from the damned other: the sick/caring couple, and all those excluded, for various reasons, from the protection of the lockdown. The experience of being closed at home with the usual cohabitants is also excluded from the new sociality, where the violence of forced family relationships emerges. There are others excluded from a maniacally friendlyus: the elderly who do not use the internet and who most of all risk dying. There is also a culture that, within the failure of habitual social relations, underlines the powerlessness of institutions (political, health, media, etc.) in the pandemic contingency. Finally, there is a pre-lockdown culture, made up of fear that will lead to chooseisolation. In the data, the productive world is missing, which for those interviewed by the research did not find -in the period of time we considered -a shared emotional code that could be gathered in a cluster. The research also had an intervention objective: to create a context in which the pandemicevent could be interpreted, within a setting of participation. In addition to publishing the data quickly, we intend to promote discussion groups onthe internet with participants. The creation of a sharing context is also areason for the high number of Author