637 research outputs found

    Pathwise super-replication via Vovk's outer measure

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    Since Hobson's seminal paper [D. Hobson: Robust hedging of the lookback option. In: Finance Stoch. (1998)] the connection between model-independent pricing and the Skorokhod embedding problem has been a driving force in robust finance. We establish a general pricing-hedging duality for financial derivatives which are susceptible to the Skorokhod approach. Using Vovk's approach to mathematical finance we derive a model-independent super-replication theorem in continuous time, given information on finitely many marginals. Our result covers a broad range of exotic derivatives, including lookback options, discretely monitored Asian options, and options on realized variance.Comment: 18 page

    GALA-n: Generic Architecture of Layout-Aware n-Bit Quantum Operators for Cost-Effective Realization on IBM Quantum Computers

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    A generic architecture of n-bit quantum operators is proposed for cost-effective transpilation, based on the layouts and the number of n neighbor physical qubits for IBM quantum computers, where n >= 3. This proposed architecture is termed "GALA-n quantum operator". The GALA-n quantum operator is designed using the visual approach of the Bloch sphere, from the visual representations of the rotational quantum operations for IBM native gates (square root of X, X, RZ, and CNOT). In this paper, we also proposed a new formula for the quantum cost, which calculates the total numbers of native gates, SWAP gates, and the depth of the final transpiled quantum circuits. This formula is termed the "transpilation quantum cost". After transpilation, our proposed GALA-n quantum operator always has a lower transpilation quantum cost than that of conventional n-bit quantum operators, which are mainly constructed from costly n-bit Toffoli gates.Comment: 27 pages, 22 figure

    Canonical multi-valued input Reed-Muller trees and forms

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    There is recently an increased interest in logic synthesis using EXOR gates. The paper introduces the fundamental concept of Orthogonal Expansion, which generalizes the ring form of the Shannon expansion to the logic with multiple-valued (mv) inputs. Based on this concept we are able to define a family of canonical tree circuits. Such circuits can be considered for binary and multiple-valued input cases. They can be multi-level (trees and DAG's) or flattened to two-level AND-EXOR circuits. Input decoders similar to those used in Sum of Products (SOP) PLA's are used in realizations of multiple-valued input functions. In the case of the binary logic the family of flattened AND-EXOR circuits includes several forms discussed by Davio and Green. For the case of the logic with multiple-valued inputs, the family of the flattened mv AND-EXOR circuits includes three expansions known from literature and two new expansions

    An efficient and effective approach to column-based input/output encoding in functional decomposition

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    Fault Models for Quantum Mechanical Switching Networks

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    The difference between faults and errors is that, unlike faults, errors can be corrected using control codes. In classical test and verification one develops a test set separating a correct circuit from a circuit containing any considered fault. Classical faults are modelled at the logical level by fault models that act on classical states. The stuck fault model, thought of as a lead connected to a power rail or to a ground, is most typically considered. A classical test set complete for the stuck fault model propagates both binary basis states, 0 and 1, through all nodes in a network and is known to detect many physical faults. A classical test set complete for the stuck fault model allows all circuit nodes to be completely tested and verifies the function of many gates. It is natural to ask if one may adapt any of the known classical methods to test quantum circuits. Of course, classical fault models do not capture all the logical failures found in quantum circuits. The first obstacle faced when using methods from classical test is developing a set of realistic quantum-logical fault models. Developing fault models to abstract the test problem away from the device level motivated our study. Several results are established. First, we describe typical modes of failure present in the physical design of quantum circuits. From this we develop fault models for quantum binary circuits that enable testing at the logical level. The application of these fault models is shown by adapting the classical test set generation technique known as constructing a fault table to generate quantum test sets. A test set developed using this method is shown to detect each of the considered faults.Comment: (almost) Forgotten rewrite from 200

    Experimental setup and procedure for the measurement of the 7Be(n,p)7Li reaction at n_TOF

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    Following the completion of the second neutron beam line and the related experimental area (EAR2) at the n_TOF spallation neutron source at CERN, several experiments were planned and performed. The high instantaneous neutron flux available in EAR2 allows to investigate neutron induced reactions with charged particles in the exit channel even employing targets made out of small amounts of short-lived radioactive isotopes. After the successful measurement of the 7Be(n,) cross section, the 7Be(n,p)7Li reaction was studied in order to provide still missing cross section data of relevance for Big Bang Nucleosynthesis (BBN), in an attempt to find a solution to the cosmological Lithium abundance problem. This paper describes the experimental setup employed in such a measurement and its characterization.Séptimo Programa Marco de la Comunidad Europea de la Energía Atómica (Euratom)-Proyecto CHANDA (No. 605203)Narodowe Centrum Nauki (NCN)-UMO-2012/04/M/ST2/00700-UMO-2016/22/M/ST2/00183Croatian Science Foundation-HRZZ 168

    Gas electron tracking detector for beta decay experiments

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    For identification and 3D-tracking of low-energy electrons a new type of gas-based detector was designed that minimizes scattering and energy loss. The current version of the detector is a combination of a plastic scintillator, serving as a trigger source and energy detector, and a hexagonally structured multi-wire drift chamber (MWDC), filled with a mixture of helium and isobutane gas. The drift time information is used to track particles in the plane perpendicular to the wires, while a charge division technique provides spatial information along the wires. The gas tracker was successfully used in the miniBETA project as a beta spectrometer for a measurement of the weak magnetism form factor in nuclear beta decay. The precision of the three-dimensional electron tracking, in combination with low-mass, low-Z materials and identification of backscattering from scintillator, facilitated a reduction of the main systematics effects. At certain conditions, a spatial resolution better than 0.5 mm was obtained in the plane perpendicular to the wires, while resolutions of about 6 mm were achieved along wires. Thanks to precise tracking information, it is possible to eliminate electrons and other particles not originating from the desired decay with high efficiency. Additionally, using the coincidence between MWDC and scintillator, background from gamma emission typically accompanying radioactive decays, was highly suppressed. An overview of different event topologies is presented together with the tracker's ability to correctly recognize them. The analysis is supported by Monte Carlo simulations using Geant4 and Garfield++ packages. Finally, the preliminary results from the 114In spectrum study are presented.Comment: 5 pages, 3 figures, accepted for publication in JINST - PSD12(2021
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