Thermal correlators of anyons in two dimensions

The anyon fields have trivial $\alpha$-commutator for $\alpha$ not integer. For integer $\alpha$ the commutators become temperature-dependent operator valued distributions. The $n$-point functions do not factorize as for quasifree states.Comment: 14 pages, LaTeX (misprints corrected, a reference added

SiPM and front-end electronics development for Cherenkov light detection

The Italian Institute of Nuclear Physics (INFN) is involved in the development of a demonstrator for a SiPM-based camera for the Cherenkov Telescope Array (CTA) experiment, with a pixel size of 6$\times$6 mm$^2$. The camera houses about two thousands electronics channels and is both light and compact. In this framework, a R&D program for the development of SiPMs suitable for Cherenkov light detection (so called NUV SiPMs) is ongoing. Different photosensors have been produced at Fondazione Bruno Kessler (FBK), with different micro-cell dimensions and fill factors, in different geometrical arrangements. At the same time, INFN is developing front-end electronics based on the waveform sampling technique optimized for the new NUV SiPM. Measurements on 1$\times$1 mm$^2$, 3$\times$3 mm$^2$, and 6$\times$6 mm$^2$ NUV SiPMs coupled to the front-end electronics are presentedComment: In Proceedings of the 34th International Cosmic Ray Conference (ICRC2015), The Hague, The Netherlands. All CTA contributions at arXiv:1508.0589

Portfolio selection problems in practice: a comparison between linear and quadratic optimization models

Several portfolio selection models take into account practical limitations on the number of assets to include and on their weights in the portfolio. We present here a study of the Limited Asset Markowitz (LAM), of the Limited Asset Mean Absolute Deviation (LAMAD) and of the Limited Asset Conditional Value-at-Risk (LACVaR) models, where the assets are limited with the introduction of quantity and cardinality constraints. We propose a completely new approach for solving the LAM model, based on reformulation as a Standard Quadratic Program and on some recent theoretical results. With this approach we obtain optimal solutions both for some well-known financial data sets used by several other authors, and for some unsolved large size portfolio problems. We also test our method on five new data sets involving real-world capital market indices from major stock markets. Our computational experience shows that, rather unexpectedly, it is easier to solve the quadratic LAM model with our algorithm, than to solve the linear LACVaR and LAMAD models with CPLEX, one of the best commercial codes for mixed integer linear programming (MILP) problems. Finally, on the new data sets we have also compared, using out-of-sample analysis, the performance of the portfolios obtained by the Limited Asset models with the performance provided by the unconstrained models and with that of the official capital market indices

Evolution Kernels of Twist-3 Light-Ray Operators in Polarized Deep Inelastic Scattering

The twist three contributions to the $Q^2$-evolution of the spin-dependent structure function $g_2(x)$ are considered in the non-local operator product approach. Starting from the perturbative expansion of the T-product of two electromagnetic currents, we introduce the nonlocal light-cone expansion proved by Anikin and Zavialov and determine the physical relevant set of light-ray operators of twist three. Using the equations of motion we show the equivalence of these operators to the Shuryak-Vainshtein operators plus the mass operator, and we determine their evolution kernels using the light-cone gauge with the Leibbrandt-Mandelstam prescription. The result of Balitsky and Braun for the twist three evolution kernel (nonsinglet case) is confirmed.Comment: 7 pages, LaTeX, Talk given at the workshop "QCD and QED in Higher Order", Rheinsberg, April 21-26, 199

Regularizing Portfolio Optimization

The optimization of large portfolios displays an inherent instability to estimation error. This poses a fundamental problem, because solutions that are not stable under sample fluctuations may look optimal for a given sample, but are, in effect, very far from optimal with respect to the average risk. In this paper, we approach the problem from the point of view of statistical learning theory. The occurrence of the instability is intimately related to over-fitting which can be avoided using known regularization methods. We show how regularized portfolio optimization with the expected shortfall as a risk measure is related to support vector regression. The budget constraint dictates a modification. We present the resulting optimization problem and discuss the solution. The L2 norm of the weight vector is used as a regularizer, which corresponds to a diversification "pressure". This means that diversification, besides counteracting downward fluctuations in some assets by upward fluctuations in others, is also crucial because it improves the stability of the solution. The approach we provide here allows for the simultaneous treatment of optimization and diversification in one framework that enables the investor to trade-off between the two, depending on the size of the available data set

Anyons and the Bose-Fermi duality in the finite-temperature Thirring model

Solutions to the Thirring model are constructed in the framework of algebraic QFT. It is shown that for all positive temperatures there are fermionic solutions only if the coupling constant is $\lambda=\sqrt{2(2n+1)\pi}, n\in {\bf N}$. These fermions are inequivalent and only for $n=1$ they are canonical fields. In the general case solutions are anyons. Different anyons (which are uncountably many) live in orthogonal spaces and obey dynamical equations (of the type of Heisenberg's "Urgleichung") characterized by the corresponding values of the statistic parameter. Thus statistic parameter turns out to be related to the coupling constant $\lambda$ and the whole Hilbert space becomes non-separable with a different "Urgleichung" satisfied in each of its sectors. This feature certainly cannot be seen by any power expansion in $\lambda$. Moreover, since the latter is tied to the statistic parameter, it is clear that such an expansion is doomed to failure and will never reveal the true structure of the theory. The correlation functions in the temperature state for the canonical dressed fermions are shown by us to coincide with the ones for bare fields, that is in agreement with the uniqueness of the $\tau$-KMS state over the CAR algebra ($\tau$ being the shift automorphism). Also the $\alpha$-anyon two-point function is evaluated and for scalar field it reproduces the result that is known from the literature.Comment: 25 pages, LaTe

Fashion, Cooperation, and Social Interactions

Fashion plays such a crucial rule in the evolution of culture and society that it is regarded as a second nature to the human being. Also, its impact on economy is quite nontrivial. On what is fashionable, interestingly, there are two viewpoints that are both extremely widespread but almost opposite: conformists think that what is popular is fashionable, while rebels believe that being different is the essence. Fashion color is fashionable in the first sense, and Lady Gaga in the second. We investigate a model where the population consists of the afore-mentioned two groups of people that are located on social networks (a spatial cellular automata network and small-world networks). This model captures two fundamental kinds of social interactions (coordination and anti-coordination) simultaneously, and also has its own interest to game theory: it is a hybrid model of pure competition and pure cooperation. This is true because when a conformist meets a rebel, they play the zero sum matching pennies game, which is pure competition. When two conformists (rebels) meet, they play the (anti-) coordination game, which is pure cooperation. Simulation shows that simple social interactions greatly promote cooperation: in most cases people can reach an extraordinarily high level of cooperation, through a selfish, myopic, naive, and local interacting dynamic (the best response dynamic). We find that degree of synchronization also plays a critical role, but mostly on the negative side. Four indices, namely cooperation degree, average satisfaction degree, equilibrium ratio and complete ratio, are defined and applied to measure people's cooperation levels from various angles. Phase transition, as well as emergence of many interesting geographic patterns in the cellular automata network, is also observed.Comment: 21 pages, 12 figure

Form factors in the Bullough-Dodd related models: The Ising model in a magnetic field

We consider particular modification of the free-field representation of the form factors in the Bullough-Dodd model. The two-particles minimal form factors are excluded from the construction. As a consequence, we obtain convenient representation for the multi-particle form factors, establish recurrence relations between them and study their properties. The proposed construction is used to obtain the free-field representation of the lightest particles form factors in the $\Phi_{1,2}$ perturbed minimal models. As a significant example we consider the Ising model in a magnetic field. We check that the results obtained in the framework of the proposed free-field representation are in agreement with the corresponding results obtained by solving the bootstrap equations.Comment: 20 pages; v2: some misprints, textual inaccuracies and references corrected; some references and remarks adde

HMM based scenario generation for an investment optimisation problem

This is the post-print version of the article. The official published version can be accessed from the link below - Copyright @ 2012 Springer-Verlag.The Geometric Brownian motion (GBM) is a standard method for modelling financial time series. An important criticism of this method is that the parameters of the GBM are assumed to be constants; due to this fact, important features of the time series, like extreme behaviour or volatility clustering cannot be captured. We propose an approach by which the parameters of the GBM are able to switch between regimes, more precisely they are governed by a hidden Markov chain. Thus, we model the financial time series via a hidden Markov model (HMM) with a GBM in each state. Using this approach, we generate scenarios for a financial portfolio optimisation problem in which the portfolio CVaR is minimised. Numerical results are presented.This study was funded by NET ACE at OptiRisk Systems