Number Of Final States Research Articles

Efficiency of Dynamic Portfolio Choices: An Experiment

Abstract We study the efficiency of dynamic portfolio choices using the nonparametric methods of Dybvig (1988) and Post (2003). We compare a dynamic portfolio task against an equivalent static Arrow-Debreu problem under two alternative environments: (1) nonpooled with $2^T$ terminal states and (2) pooled with $T+1$ unique terminal states. The results suggest that, within each environment, efficiency is lower in a static format and when the number of final states is larger. In the nonpooled dynamic task, which allows for path dependent strategies, we find that a form of stop-loss strategy drives efficiency losses.

Signatures of R˜2 class of leptoquarks at the upcoming ep colliders

We explore the signatures of the $\tilde{R}_2$ class of leptoquark (LQ) models at the proposed $e^- p$ and $e^+p$ colliders. We carry out an analysis for the proposed colliders LHeC and FCC-eh with center of mass (c.m.) energy 1.3 TeV and 3.46 TeV, respectively. For $\tilde{R}_2$ class of LQ models, there are a number of final states that can arise from LQ production and its subsequent decay. In this report we do a detailed cut-based analysis for the $l^{\pm}j$ final state. We also discuss the effect of polarized electron and positron beams on LQ production and in turn on $l^{\pm}j$ production. At LHeC, the final state $l^+j$ has very good discovery prospect. We find that, only 100 $\text{fb}^{-1}$ of data can probe LQ mass upto 1.2 TeV with $5\sigma$ significance, even with a generic set of cuts. On the contrary, at FCC-eh, one can probe LQ masses upto 2.2 TeV (for $e^-$ beam) and 3 TeV (for $e^+$ beam), at more than $5\sigma$ significance with luminosity $1000\,\text{fb}^{-1}$ and $500\,\text{fb}^{-1}$, respectively.

Application of Bayesian Networks to Quantitative Assessment of Safety Barriers’ Performance in the Prevention of Major Accidents

Process plants are particularly subjected to major accidental events, whose catastrophic escalations, triggered by external factors and characterized by very high impact and low probability, can affect both workers and population in the nearby of a process facility, as well as assets and environment. In the context of major accidents prevention, control and mitigation, safety barriers are widely employed; nevertheless, concerning their quantitative assessment, only availability is generally accounted as a measure of their performances and a frequency-based approach is applied. Recent applications have highlighted the potential of Bayesian Networks, a graphical probabilistic method, in major accidents modelling and prevention. This contribution is aimed at applying Bayesian Networks to quantitative assessment of safety barriers’ performance in the context of major accidents prevention within the process industry. The Bayesian approach will be compared with a conventional Event-Tree based one by the application to an illustrative case study, considering a major accident whose occurrence can be prevented by the action of several pertinent technical safety barriers. In the Bayesian approach, safety barriers performance has been assessed by means of specific gates, depending on barriers states and classification. An adequate number of final states has been considered. The conversion of the Event-Tree, key element of the conventional frequency-based approach, into a Bayesian Network has been performed, with the aim to test the ability of Bayesian Networks in representing possible events sequences. Indeed, the potentialities of the Bayesian approach in revising probabilities have been explored by means of two different techniques: probability updating and probability adapting. In probability updating, the information about one of the outcomes is used as an evidence, determining the most probable explanation, leading to that specific final state. In probability adapting, additional information during a time interval, in the form of accident sequence precursors, are inserted in the analysis, in purpose to revise safety barriers’ performances and final events probabilities. The results of the case study will highlight the advantages of a Bayesian approach to safety barriers’ performance assessment, proving that its application may eventually will turn into a more flexible and realistic analysis of major accidental scenarios, in comparison with conventional techniques.

The complexity of intersecting finite automata having few final states

The problem of determining whether several finite automata accept a word in common is closely related to the well-studied membership problem in transformation monoids. We raise the issue of limiting the number of final states in the automata intersection problem. For automata with two final states, we show the problem to be $${\oplus}$$źL-complete or NP-complete according to whether a nontrivial monoid other than a direct product of cyclic groups of order 2 is allowed in the automata. We further consider idempotent commutative automata and (Abelian, mainly) group automata with one, two, or three final states over a singleton or larger alphabet, elucidating (under the usual hypotheses on complexity classes) the complexity of the intersection nonemptiness and related problems in each case.

Dependence of the intrinsic line width of surface states on the wave vector: The Cu(111) and Ag(111) surfaces

The dependence of the intrinsic line width Γ of electron and hole states due to inelastic scattering on the wave vector k∥ in the occupied surface state and the first image potential state on the Cu(111) and Ag(111) surfaces has been calculated using the GW approximation, which simulates the self-energy of the quasiparticles by the product of the Greens’s function and the dynamically screened Coulomb potential. Different contributions to the relaxation of electron and hole excitations have been analyzed. It has been demonstrated that, for both surfaces, the main channel of relaxation of holes in the occupied surface states is intraband scattering and that, for electrons in the image potential states, the interband transitions play a decisive role. A sharp decrease in the intrinsic line width of the hole state with an increase in k∥ is caused by a decrease in the number of final states, whereas an increase in Γ of the image potential state is predominantly determined by an increase of its overlap with bulk states.

Final state-selected spectra in unimolecular reactions: A transition-state-based random matrix model for overlapping resonances

Final state-selected spectra in unimolecular decomposition are obtained by a random matrix version of Feshbach’s optical model. The number of final states which are independently coupled to the molecular quasibound states is identified with the number of states at the dividing surface of transition state theory (TST). The coupling of the transition state to the molecular complex is modeled via a universal random matrix effective Hamiltonian which is characterized by its resonance eigenstates and provides the correct average unimolecular decay rate. The transition from nonoverlapping resonances which are associated with isolated Lorentzian spectral peaks, to overlapping resonances, associated with more complex spectra, is characterized in terms of deviations from a χ2-like distribution of the resonance widths and the approach to a random phase-distribution of the resonance scattering amplitudes. The evolution of the system from a tight transition state to reaction products is treated explicitly as a scattering process where specific dynamics can be incorporated. Comparisons with recently measured final state-selected spectra and rotational distributions for the unimolecular reaction of NO2 show that the present model provides a useful new approach for understanding and interpreting experimental results which are dominated by overlapping resonances.

Collisional perturbation of quantum regular and irregular intramolecular states: State-to-state study of a model

Abstract State-to-state analysis is presented of collisional energy transfer in quantum-mechanical collinear collisions between an atom and a triatomic molecule. The molecular potential was that of Henon and Heiles, while the interaction was modelled by both a soft, exponential repulsive potential and a Morse potential. This analysis emphasizes how different categories of molecular states (normal mode, local mode, or mode mixed) are influenced by the collision perturbation. The discussion centers around plots showing the energy dependence of P ??? ( X ), the probability that initial state i ends up in category X , and contour maps of state-to-state transition probabilities, P ??? ( E ). For the exponential repulsive model, there is a resistance to alteration of the molecular energy; “horizontal” transitions occur within bands of quasi-resonant states. By way of contrast, the Morse interaction model exhibits many vertical transitions, with many low-intensity transitions to a large number of final states. The special role played by extreme motion states, emphasized in recent studies by Hose and Taylor, is discussed in relation to their survivability. Finally, these results are related to trends that we found earlier in the energy dependence of the average energy transfer.

Direct and collective captures of energetic neutrons by ellipsoidally deformed nuclei

Abstract The direct and collective theories for nucleon radiative capture are applied to the ellipsoidally deformed nucleus within the framework of an adiabatic approximation. A volume-type form factor rf ( r ) is used for the particle-vibration coupling Hamiltonian between a projectile and the E1 vibrational mode of a target nucleus. Numerical application is made for the 238 U(n, γ) 239 U reaction with 5 to 20 MeV neutrons. Contributions to the capture cross section from the rotational bands for all Nilsson levels in 239 U are calculated to produce the excitation curve and capture γ-ray spectra for this reaction. The coupling strength is taken to be 110 MeV and the deformation parameter to be 0.268, with only the Y 2 deformation of the target nucleus being taken into consideration. Good agreement is obtained between the calculated cross sections and the observed data. Discussions are given for some ambiguities in the calculation, i.e. the depth of the central part of an optical potential, the coupling strength, the giant resonance parameters, and the number of final states of a captured nucleon in the residual nucleus. The number of Nilsson levels and the members belonging to each rotational band chosen, strongly influence the results of the calculations.

Thermal Conductivity of Solids. III. Modification of Three-Phonon Processes by Isotopic Scattering

The experimental observation that the effective strength of the phonon-phonon scattering in Ge-Si mixtures increases with the disorder parameter is explained qualitatively and semi-quantitatively by means of second-order interactions in which the three-phonon processes are modified by isotopic scattering. This effect is large because of the occurrence of small-energy denominators and the increased number of final states resulting from the over-all nonconservation of crystal momentum for such three-phonon processes.