On the Form Factors of Relevant Operators and their Cluster Property

We compute the Form Factors of the relevant scaling operators in a class of integrable models without internal symmetries by exploiting their cluster properties. Their identification is established by computing the corresponding anomalous dimensions by means of Delfino--Simonetti--Cardy sum--rule and further confirmed by comparing some universal ratios of the nearby non--integrable quantum field theories with their independent numerical determination.Comment: Latex file, 35 pages with 5 Postscript figure

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

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

Universal Ratios in the 2-D Tricritical Ising Model

We consider the universality class of the two-dimensional Tricritical Ising Model. The scaling form of the free-energy naturally leads to the definition of universal ratios of critical amplitudes which may have experimental relevance. We compute these universal ratios by a combined use of results coming from Perturbed Conformal Field Theory, Integrable Quantum Field Theory and numerical methods.Comment: 4 pages, LATEX fil

The DarkSide experiment

DarkSide is a dark matter direct search experiment at Laboratori Nazionali del Gran Sasso (LNGS). DarkSide is based on the detection of rare nuclear recoils possibly induced by hypothetical dark matter particles, which are supposed to be neutral, massive (m>10GeV) and weakly interactive (WIMP). The dark matter detector is a two-phase time projection chamber (TPC) filled with ultra-pure liquid argon. The TPC is placed inside a muon and a neutron active vetoes to suppress the background. Using argon as active target has many advantages, the key features are the strong discriminant power between nuclear and electron recoils, the spatial reconstruction and easy scalability to multi-tons size. At the moment DarkSide-50 is filled with ultra-pure argon, extracted from underground sources, and from April 2015 it is taking data in its final configuration. When combined with the preceding search with an atmospheric argon target, it is possible to set a 90% CL upper limit on the WIMP-nucleon spin-independent cross section of 2.0×10−44 cm2 for a WIMP mass of 100GeV/c2. The next phase of the experiment, DarkSide-20k, will be the construction of a new detector with an active mass of ∼ 20 tons

Estimating Portfolio Risk for Tail Risk Protection Strategies

We forecast portfolio risk for managing dynamic tail risk protection strategies, based on extreme value theory, expectile regression, Copula-GARCH and dynamic GAS models. Utilizing a loss function that overcomes the lack of elicitability for Expected Shortfall, we propose a novel Expected Shortfall (and Value-at-Risk) forecast combination approach, which dominates simple and sophisticated standalone models as well as a simple average combination approach in modelling the tail of the portfolio return distribution. While the associated dynamic risk targeting or portfolio insurance strategies provide effective downside protection, the latter strategies suffer less from inferior risk forecasts given the defensive portfolio insurance mechanics

Analytic Representation of Finite Quantum Systems

A transform between functions in R and functions in Zd is used to define the analogue of number and coherent states in the context of finite d-dimensional quantum systems. The coherent states are used to define an analytic representation in terms of theta functions. All states are represented by entire functions with growth of order 2, which have exactly d zeros in each cell. The analytic function of a state is constructed from its zeros. Results about the completeness of finite sets of coherent states within a cell are derived

Exact correlation functions of Bethe lattice spin models in external fields

We develop a transfer matrix method to compute exactly the spin-spin correlation functions of Bethe lattice spin models in the external magnetic field h and for any temperature T. We first compute the correlation function for the most general spin - S Ising model, which contains all possible single-ion and nearest-neighbor pair interactions. This general spin - S Ising model includes the spin-1/2 simple Ising model and the Blume-Emery-Griffiths (BEG) model as special cases. From the spin-spin correlation functions, we obtain functions of correlation length for the simple Ising model and BEG model, which show interesting scaling and divergent behavior as T approaches the critical temperature. Our method to compute exact spin-spin correlation functions may be applied to other Ising-type models on Bethe and Bethe-like lattices.Comment: 19 page

Accounting for risk of non linear portfolios: a novel Fourier approach

The presence of non linear instruments is responsible for the emergence of non Gaussian features in the price changes distribution of realistic portfolios, even for Normally distributed risk factors. This is especially true for the benchmark Delta Gamma Normal model, which in general exhibits exponentially damped power law tails. We show how the knowledge of the model characteristic function leads to Fourier representations for two standard risk measures, the Value at Risk and the Expected Shortfall, and for their sensitivities with respect to the model parameters. We detail the numerical implementation of our formulae and we emphasizes the reliability and efficiency of our results in comparison with Monte Carlo simulation.Comment: 10 pages, 12 figures. Final version accepted for publication on Eur. Phys. J.