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We generalize a semi-classical path integral approach originally introduced by Giachetti and Tognetti [Phys. Rev. Lett. 55, 912 (1985)] and Feynman and Kleinert [Phys. Rev. A 34, 5080 (1986)] to time-dependent Hamiltonians, thus extending the scope of the method to the pricing of financial derivatives. We illustrate the accuracy of the approach by presenting results for the well-known, but analytically intractable, Black-Karasinski model for the dynamics of interest rates. The accuracy and computational efficiency of this path integral approach makes it a viable alternative to fully-numerical schemes for a variety of applications in derivatives pricing., Comment: 13 pages

The click-based interactive segmentation aims to extract the object of interest from an image with the guidance of user clicks. Recent work has achieved great overall performance by employing feedback from the output. However, in most state-of-the-art approaches, 1) the inference stage involves inflexible heuristic rules and requires a separate refinement model, and 2) the number of user clicks and model performance cannot be balanced. To address the challenges, we propose a click-based and mask-guided interactive image segmentation framework containing three novel components: Cascade-Forward Refinement (CFR), Iterative Click Loss (ICL), and SUEM image augmentation. The CFR offers a unified inference framework to generate segmentation results in a coarse-to-fine manner. The proposed ICL allows model training to improve segmentation and reduce user interactions simultaneously. The proposed SUEM augmentation is a comprehensive way to create large and diverse training sets for interactive image segmentation. Extensive experiments demonstrate the state-of-the-art performance of the proposed approach on five public datasets. Remarkably, our model reduces by 33.2\%, and 15.5\% the number of clicks required to surpass an IoU of 0.95 in the previous state-of-the-art approach on the Berkeley and DAVIS sets, respectively.

U-10Zr-based nuclear fuel is pursued as a primary candidate for next-generation sodium-cooled fast reactors. However, more advanced characterization and analysis are needed to form a fundamental understating of the fuel performance, and make U-10Zr fuel qualify for commercial use. The movement of lanthanides across the fuel section from the hot fuel center to the cool cladding surface is one of the key factors to affect fuel performance. In the advanced annular U-10Zr fuel, the lanthanides present as fission gas bubbles. Due to a lack of annotated data, existing literature utilized a multiple-threshold method to separate the bubbles and calculate bubble statistics on an annular fuel. However, the multiple-threshold method cannot achieve robust performance on images with different qualities and contrasts, and cannot distinguish different bubbles. This paper proposes a hybrid framework for efficient bubble segmentation. We develop a bubble annotation tool and generate the first fission gas bubble dataset with more than 3000 bubbles from 24 images. A multi-task deep learning network integrating U-Net and ResNet is designed to accomplish instance-level bubble segmentation. Combining the segmentation results and image processing step achieves the best recall ratio of more than 90% with very limited annotated data. Our model shows outstanding improvement by comparing the previously proposed thresholding method. The proposed method has promising to generate a more accurate quantitative analysis of fission gas bubbles on U-10Zr annular fuels. The results will contribute to identifying the bubbles with lanthanides and finally build the relationship between the thermal gradation and lanthanides movements of U-10Zr annular fuels. Mover, the deep learning model is applicable to other similar material micro-structure segmentation tasks., Comment: 9 figures, 3 tables

U-10Zr-based metallic nuclear fuel is a promising fuel candidate for next-generation sodium-cooled fast reactors.The research experience of the Idaho National Laboratory for this type of fuel dates back to the 1960s. Idaho National Laboratory researchers have accumulated a considerable amount of experience and knowledge regarding fuel performance at the engineering scale. The limitation of advanced characterization and lack of proper data analysis tools prevented a mechanistic understanding of fuel microstructure evolution and properties degradation during irradiation. This paper proposed a new workflow, coupled with domain knowledge obtained by advanced post-irradiation examination methods, to provide unprecedented and quantified insights into the fission gas bubbles and pores, and lanthanide distribution in an annular fuel irradiated in the Advanced Test Reactor. In the study, researchers identify and confirm that the Zr-bearing secondary phases exist and generate the quantitative ratios of seven microstructures along the thermal gradient. Moreover, the distributions of fission gas bubbles on two samples of U-10Zr advanced fuels were quantitatively compared. Conclusive findings were obtained and allowed for evaluation of the lanthanide transportation through connected bubbles based on approximately 67,000 fission gas bubbles of the two advanced samples., Comment: 21 pages, 12 figures

TurboRVB is a computational package for {\it ab initio} Quantum Monte Carlo (QMC) simulations of both molecular and bulk electronic systems. The code implements two types of well established QMC algorithms: Variational Monte Carlo (VMC), and Diffusion Monte Carlo in its robust and efficient lattice regularized variant. A key feature of the code is the possibility of using strongly correlated many-body wave functions. The electronic wave function (WF) is obtained by applying a Jastrow factor, which takes into account dynamical correlations, to the most general mean-field ground state, written either as an antisymmetrized geminal product with spin-singlet pairing, or as a Pfaffian, including both singlet and triplet correlations. This wave function can be viewed as an efficient implementation of the so-called resonating valence bond (RVB) ansatz, first proposed by L. Pauling and P. W. Anderson in quantum chemistry and condensed matter physics, respectively. The RVB ansatz implemented in TurboRVB has a large variational freedom, including the Jastrow correlated Slater determinant as its simplest, but nontrivial case. Moreover, it has the remarkable advantage of remaining with an affordable computational cost, proportional to the one spent for the evaluation of a single Slater determinant. The code implements the adjoint algorithmic differentiation that enables a very efficient evaluation of energy derivatives, comprising the ionic forces. Thus, one can perform structural optimizations and molecular dynamics in the canonical NVT ensemble at the VMC level. For the electronic part, a full WF optimization is made possible thanks to state-of-the-art stochastic algorithms for energy minimization. The code has been efficiently parallelized by using a hybrid MPI-OpenMP protocol, that is also an ideal environment for exploiting the computational power of modern GPU accelerators., Comment: 41 pages, 21 figures, 3 tables

We show how effective-potential path-integrals methods, stemming on a simple and nice idea originally due to Feynman and successfully employed in Physics for a variety of quantum thermodynamics applications, can be used to develop an accurate and easy-to-compute semi-analytical approximation of transition probabilities and Arrow-Debreu densities for arbitrary diffusions. We illustrate the accuracy of the method by presenting results for the Black-Karasinski and the GARCH linear models, for which the proposed approximation provides remarkably accurate results, even in regimes of high volatility, and for multi-year time horizons. The accuracy and the computational efficiency of the proposed approximation makes it a viable alternative to fully numerical schemes for a variety of derivatives pricing applications., Comment: 12 pages, 4 figures

We describe an efficient algorithm to compute forces in quantum Monte Carlo using adjoint algorithmic differentiation. This allows us to apply the space warp coordinate transformation in differential form, and compute all the 3M force components of a system with M atoms with a computational effort comparable with the one to obtain the total energy. Few examples illustrating the method for an electronic system containing several water molecules are presented. With the present technique, the calculation of finite-temperature thermodynamic properties of materials with quantum Monte Carlo will be feasible in the near future., Comment: 32 pages, 4 figure, to appear in The Journal of Chemical Physics

We show how Adjoint Algorithmic Differentiation (AAD) allows an extremely efficient calculation of correlation Risk of option prices computed with Monte Carlo simulations. A key point in the construction is the use of binning to simultaneously achieve computational efficiency and accurate confidence intervals. We illustrate the method for a copula-based Monte Carlo computation of claims written on a basket of underlying assets, and we test it numerically for Portfolio Default Options. For any number of underlying assets or names in a portfolio, the sensitivities of the option price with respect to all the pairwise correlations is obtained at a computational cost which is at most 4 times the cost of calculating the option value itself. For typical applications, this results in computational savings of several order of magnitudes with respect to standard methods., Comment: 5 pages, 2 figures

Variational wave functions containing electronic pairing and suppressed charge fluctuations (i.e., projected BCS states) have been proposed as the paradigm for disordered magnetic systems (including spin liquids). Here we discuss the general properties of these states in one and two dimensions, and show that different quantum phases may be described with high accuracy by the same class of variational wave functions, including dimerized and magnetically ordered states. In particular, phases with magnetic order may be obtained from a straightforward generalization containing both antiferromagnetic and superconducting order parameters, as well as suitable spin Jastrow correlations. In summary, projected wave functions represent an extremely flexible tool for understanding the physics of low-dimensional magnetic systems., Comment: Lecture notes for Trieste Summer School, August 2007. To appear

We investigate the use of Antithetic Variables, Control Variates and Importance Sampling to reduce the statistical errors of option sensitivities calculated with the Likelihood Ratio Method in Monte Carlo. We show how Antithetic Variables solve the well-known problem of the divergence of the variance of Delta for short maturities and small volatilities. With numerical examples within a Gaussian Copula framework, we show how simple Control Variates and Importance Sampling strategies provide computational savings up to several orders of magnitude., Comment: 4 pages, 2 figures

A recently introduced Importance Sampling strategy based on a least squares optimization is applied to the Monte Carlo simulation of Libor Market Models. Such Least Squares Importance Sampling (LSIS) allows the automatic optimization of the sampling distribution within a trial class by means of a quick presimulation algorithm of straightforward implementation. With several numerical examples we show that LSIS can be extremely effective in reducing the variance of Monte Carlo estimators often resulting, especially when combined with stratified sampling, in computational speed-ups of orders of magnitude., Comment: 14 pages, 1 figure

We describe a simple Importance Sampling strategy for Monte Carlo simulations based on a least squares optimization procedure. With several numerical examples, we show that such Least Squares Importance Sampling (LSIS) provides efficiency gains comparable to the state of the art techniques, when the latter are known to perform well. However, in contrast to traditional approaches, LSIS is not limited to the determination of the optimal mean of a Gaussian sampling distribution. As a result, it outperforms other methods when the ability to adjust higher moments of the sampling distribution, or to deal with non-Gaussian or multi-modal densities, is critical to achieve variance reductions., Comment: 12 pages, 4 figures

In this paper we discuss a closed-form approximation of the likelihood functions of an arbitrary diffusion process. The approximation is based on an exponential ansatz of the transition probability for a finite time step $\Delta t$, and a series expansion of the deviation of its logarithm from that of a Gaussian distribution. Through this procedure, dubbed {\em exponent expansion}, the transition probability is obtained as a power series in $\Delta t$. This becomes asymptotically exact if an increasing number of terms is included, and provides remarkably accurate results even when truncated to the first few (say 3) terms. The coefficients of such expansion can be determined straightforwardly through a recursion, and involve simple one-dimensional integrals. We present several examples of financial interest, and we compare our results with the state-of-the-art approximation of discretely sampled diffusions [A\"it-Sahalia, {\it Journal of Finance} {\bf 54}, 1361 (1999)]. We find that the exponent expansion provides a similar accuracy in most of the cases, but a better behavior in the low-volatility regime. Furthermore the implementation of the present approach turns out to be simpler. Within the functional integration framework the exponent expansion allows one to obtain remarkably good approximations of the pricing kernels of financial derivatives. This is illustrated with the application to simple path-dependent interest rate derivatives. Finally we discuss how these results can also be used to increase the efficiency of numerical (both deterministic and stochastic) approaches to derivative pricing., Comment: 28 pages, 7 figures

We show strong numerical evidence in favor of an unexpected virtually gapless spectrum, with edge states localized at the boundaries, in frustrated spin-1/2 antiferromagnetic ladders with an odd number of legs. These features can be accurately reproduced by using a projected BCS wave function with a non-trivial pairing, that mixes even and odd reflection symmetries. This approach gives the correct classification of the excitations and provides a simple and very appealing picture of an unconventional spin-liquid phase stabilized by frustration., Comment: 4 pages and 4 figures

A computational technique borrowed from the physical sciences is introduced to obtain accurate closed-form approximations for the transition probability of arbitrary diffusion processes. Within the path integral framework the same technique allows one to obtain remarkably good approximations of the pricing kernels of financial derivatives. Several examples are presented, and the application of these results to increase the efficiency of numerical approaches to derivative pricing is discussed., Comment: 21 pages, 5 figures, to appear in the International Journal of Theoretical and Applied Finance

We explore the effect of local charge fluctuations on the spin response of a Mott insulator by deriving an effective spin model, and studying it using Schwinger boson mean field theory. Applying this to La$_2$CuO$_4$, we show that an accurate fit to the magnon dispersion relation, measured by Coldea {\em et al.} [Phys. Rev. Lett. {\bf 86}, 5377 (2001)] is obtained with Hubbard model parameters $U \approx 2.34 eV$, and $t \approx 360 meV$. These parameters lead to estimates of the staggered magnetization ($m_s \approx 0.25$), spin wave velocity ($c\approx 800 meV$-\AA), and spin stiffness ($\rho_s \approx 24 meV$). In particular the staggered moment as well as the effective local moment are renormalized to smaller values compared to the Heisenberg model due to local charge fluctuations in the Hubbard model. The dynamical structure factor shows considerable weight in the continuum along the zone boundary as well as secondary peaks that may be observed in high resolution neutron scattering experiments., Comment: Manuscript considerably revised following referee comments. Also added a brief discussion of sum rules. 8 pages, 6 eps figures

Projected-BCS wave functions have been proposed as the paradigm for the understanding of disordered spin states (spin liquids). Here we investigate the properties of these wave functions showing how Luttinger liquids, dimerized states, and gapped spin liquids may be described by the same class of wave functions, which, therefore, represent an extremely flexible variational tool. A close connection between spin liquids and, Comment: to be published in "Highlights in the quantum theory of condensed matter", to celebrate Mario Tosi on his 72nd birthday

Over the years the research group in Firenze has produced a number of theoretical results concerning the statistical mechanics of quantum antiferromagnetic models, which range from the theory of two-magnon Raman scattering to the characterization of the phase transitions in quantum low-dimensional antiferromagnetic models. Our research activity was steadily aimed to the understanding of experimental observations., Comment: 20 pages, 21 figures, submitted to Low Temp. Phys