Resolution Of Degeneracy Research Articles

Effect of Sterile Phases on Degeneracy Resolution Capabilities of LBL Experiments

In sterile neutrino (3+1) parameterisation, we observe that sterile phases ($\delta_{14},\delta_{24}$) are always together in oscillation probability, even when the MSW effect is considered. We see that the difference between the sterile phases has a more dominating effect over event rates compared to small variations due to changes in individual values. In this work, we show the value of sterile phase difference ($\delta_{14}-\delta_{24}$) that least affects the parameter degeneracy resolution of $\delta_{13},\theta_{23}$ at long-baseline experiments.

Potential of octant degeneracy resolution in JUNO * * Supported by the China Postdoctoral Science Foundation (2018M643283), the National Key R&D program of China ( 2018YFA0404103) and the National Natural Science Foundation of China (NSFC) (11775315)

This work extends the idea of using a cyclotron-based antineutrino source for purposes of neutrino physics. Long baseline experiments suffer from degeneracies and correlations between , and the mass hierarchy. However, the combination of a superconducting cyclotron and a big liquid scintillator detector like JUNO in a medium baseline experiment, which does not depend on the mass hierarchy, may allow to determine whether the position of the mixing angle is in the lower octant or the upper octant. Such an experiment would improve the precision of the measurement to a degree which depends on the CP-phase.

Degeneracy Resolution Capabilities of NOνA and DUNE in the Presence of Light Sterile Neutrino

We investigate the implications of a sterile neutrino on the physics potential of the proposed experiment DUNE and future runs of NOνA using latest NOνA results. Using combined analysis of the disappearance and appearance data, NOνA reported preferred solutions at normal hierarchy (NH) with two degenerate best-fit points: one in the lower octant (LO) and δ13 = 1.48π and the other in higher octant (HO) and δ13 = 0.74π. Another solution of inverted hierarchy (IH), which is 0.46σ away from best fit, was also reported. We discuss chances of resolving these degeneracies in the presence of sterile neutrino.

Effect of a light sterile neutrino at NOνA and DUNE

Now that the NOvA experiment is approaching two years run time and has released some preliminary data, some constraints for the oscillation parameters can be inferred. Currently the best fits for NOvA are three separate results, the reason they are indistinct is that they produce almost degenerate probability curves. It has been postulated that these degeneracies can be resolved by running antineutrinos at NOvA and/or combining its data with T2K. However, this degeneracy resolution power can be compromised if sterile neutrinos are present due to additional degrees of freedom that can significantly alter the oscillation probability for any of the current best fits. We aim to investigate this degradation in predictive power and the effect of the DUNE experiment on it. Now that the NOvA experiment has been running for a few years and has released some preliminary data, some constraints for the oscillation parameters can be inferred. The best fits for NOvA include three degenerate results, the reason they are indistinct is that they produce almost degenerate probability curves. It has been postulated that these degeneracies can be resolved by running antineutrinos at NOvA and/or combining its data with T2K. However, this degeneracy resolution power can be compromised if sterile neutrinos are present due to additional degrees of freedom that can significantly alter the oscillation probability for any of these best fits. We aim to investigate this degradation in predictive power and the effect of the DUNE experiment on it. In light of the 2018 NOvA data we also consider the same fits but with theta_{23}=45 to see if the sensitivity results are different.

Non-unitary lepton mixing in an inverse seesaw and its impact on the physics potential of long-baseline experiments

In this paper, we consider the low energy scale inverse seesaw mechanism in which the observed neutrino mass and lepton mixing are explained by introducing right-handed neutrinos and the gauge-singlet fermions with experimentally testable energy scale. Moreover, the presence of such new fermions leads to unitarity violation in lepton mixing due to significantly large mixing between active neutrinos and the heavy fermions. In addition to this, such large lepton mixing also gives rise to potentially large lepton flavor violation, which allows one to constrain the non-unitarity parameters via lepton flavor violating decays (li → lj γ). We make use of these constraints on non-unitarity parameters and investigate their effects on the determination of current unknown oscillation parameters at long-baseline experiments. We find that non-unitarity parameters are sensitive to the NOνA experiment. However, it is observed that the NOνA experiment is not expected to improve the current knowledge of non-unitarity parameter η21. We also find that the sensitivities to current unknowns are deteriorated significantly in the presence of non-unitary lepton mixing and these sensitivities crucially depend upon the new CP-violating phase in the non-unitary mixing. Further, we find that the degeneracy resolution capability of the NOνA experiment is reduced in the presence of non-unitarity parameters. However, the synergy between the currently running experiments T2K and NOνA can improve the parameter degeneracy resolution and hence there is enhancement in the sensitivities of unknowns.

Resolution of Degeneracy in Merton's Portfolio Problem

The Merton problem determines the optimal intertemporal portfolio choice by maximizing the expected utility, and is the basis of modern portfolio theory in continuous-time finance. However, its empirical performance is disappointing. The estimation errors of the expected rates of returns make the optimal policy degenerate, resulting in an extremely low (or unbounded) expected utility value for a high-dimensional portfolio. We further prove that the estimation error of the variance-covariance matrix leads to the degenerated policy of solely investing in the risk-free asset. This study proposes a constrained l1 - minimization approach to resolve the degeneracy. The proposed scheme can be implemented with simple linear programming and involves negligible additional computational time, compared to standard estimation. We prove the consistency of our framework that our estimate of the optimal control tends to be the true one. We also derive the rate of convergence. Simulation studies are provided to verify the finite-sample properties. An empirical study using S&P 500 component stock data demonstrates the superiority of the proposed approach.

Resolution of Degeneracy in Merton's Portfolio Problem

The Merton problem determines the optimal intertemporal portfolio choice by maximizing the expected utility and is the basis of modern portfolio theory in continuous-time finance. However, its empirical performance is disappointing. The estimation errors of the expected rates of returns make the optimal policy degenerate, resulting in an extremely low (or unbounded) expected utility value for a high-dimensional portfolio. We further prove that the estimation error of the variance-covariance matrix leads to the degenerated policy of solely investing in the risk-free asset. This study proposes a constrained $\ell_1$-minimization approach to resolve the degeneracy in the high-dimensional setting and stabilize the performance in the low-dimensional setting. The proposed scheme can be implemented with simple linear programming and involves negligible additional computational time, compared to standard estimation. We prove the consistency of our framework that our estimate of the optimal control tends to be the true one. We also derive the rate of convergence. Simulation studies are provided to verify the finite-sample properties. An empirical study using S&P 500 component stock data demonstrates the superiority of the proposed approach.

Note on Transportation Problem with New Method for Resolution of Degeneracy

Transportation algorithm minimizes the cost of transporting goods from m origins to n destinations along m*n direct routes from origin to destination. There are three methods to solve transportation problem and their solution can be further improved using Modified Distribution Method (MODI Method). This method not only checks that the solution obtained by three methods is optimal but also modify the distribution to make it optimal. The only hiccup with this method is the case of degeneracy i.e. when number of allocations less than m+n-1. In this case, we have to make the number of allocations equal to m+n-1. To remove degeneracy we allocate some cells with dummy allocations, whose value is nearly equal to zero. But, till now there is no specific rule for allocating these cells. In this study, specific method has been proposed to remove this problem of degeneracy. Thus this study helps to remove major bottle neck from transportation algorithm.

Degeneracy Resolution for Bilinear Utility Functions

Loss-aversion is a phenomenon where investors are particularly sensitive to losses and eager to avoid them. An efficient method to solve the portfolio optimization problem of maximizing the bilinear utility function is given by Best et al. (Loss-Aversion with Kinked Linear Utility Functions, CORR 2010-04, University of Waterloo, 2010). This method is useful because it performs its computations only using asset related quantities rather than much higher dimensional quantities of the LP formulation. However, a difficulty with this method is that it requires a nondegeneracy assumption which may not be satisfied. This paper implements Bland's least-index rules to the method in such a way that the efficiency of the method is retained. Then we describe the numerical results of applying our algorithm to a series of six asset problems in which the degree of loss-aversion is increased.

Physics with a very long neutrino factory baseline

We discuss the neutrino oscillation physics of a very long neutrino factory baseline over a broad range of lengths (between 6000 km and 9000 km), centered on the 'magic baseline' ({approx}7500 km) where correlations with the leptonic CP phase are suppressed by matter effects. Since the magic baseline depends only on the density, we study the impact of matter density profile effects and density uncertainties over this range, and the impact of detector locations off the optimal baseline. We find that the optimal constant density describing the physics over this entire baseline range is about 5% higher than the average matter density. This implies that the magic baseline is significantly shorter than previously inferred. However, while a single detector optimization requires fine-tuning of the (very long) baseline length, its combination with a near detector at a shorter baseline is much less sensitive to the far detector location and to uncertainties in the matter density. In addition, we point out different applications of this baseline which go beyond its excellent correlation and degeneracy resolution potential. We demonstrate that such a long baseline assists in the improvement of the {theta}{sub 13} precision and in the resolution of the octant degeneracy. Moreover, wemore » show that the neutrino data from such a baseline could be used to extract the matter density along the profile up to 0.24% at 1{sigma} for large sin{sup 2}2{theta}{sub 13}, providing a useful discriminator between different geophysical models.« less

Finite Jet Determination of Local CR Automorphisms through Resolution of Degeneracies

Let MC N be a connected real-analytic hypersurface whose Levi form is nonde- generate at some point. We prove that for every point p 2 M, there exists an integer k = k(M, p) such that germs at p of local real-analytic CR automorphisms of M are uniquely determined by their k-jets (at p). To prove this result we develop a new technique that can be seen as a resolution of the degeneracies of M. This procedure consists of blowing up M near an arbitrary point p 2 M regardless of its minimality or nonminimality; then, thanks to the blow-up, the original problem can be reduced to an analogous one for a very special class of nonminimal hypersurfaces for which one may use known techniques to prove the finite jet determination property of its CR automorphisms.

A Complementary Pivoting Approach to the Maximum Weight Clique Problem

Given an undirected graph with positive weights on the vertices, the maximum weight clique problem (MWCP) is to find a subset of mutually adjacent vertices (i.e., a clique) having largest total weight. The problem is known to be NP-hard, even to approximate. Motivated by a recent quadratic programming formulation, which generalizes an earlier remarkable result of Motzkin and Straus, in this paper we propose a new framework for the MWCP based on the corresponding linear complementarity problem (LCP). We show that, generically, all stationary points of the MWCP quadratic program exhibit strict complementarity. Despite this regularity result, however, the LCP turns out to be inherently degenerate, and we find that Lemke's well-known pivoting method, equipped with standard degeneracy resolution strategies, yields unsatisfactory experimental results. We exploit the degeneracy inherent in the problem to develop a variant of Lemke's algorithm which incorporates a new and effective look-ahead pivot rule. The resulting algorithm is tested extensively on various instances of random as well as DIMACS benchmark graphs, and the results obtained show the effectiveness of our method.

A CASSCF study of the cyclopentadienyl radical: conical intersections and the Jahn–Teller effect

The D 5 h Jahn-Teller crossing and associated C 2 v minima and saddle points in cyclopentadienyl have been optimised at the CASSCF/cc–pVDZ level of theory. The C 2 v structures were characterised by computing analytic force constants. Zero point energies calculated for all C 5H 4D and C 5HD 4 isomers of the C 2 v minima suggest an alternative interpretation of the experimentally observed degeneracy resolution (L. Yu, D.W. Cullin, J.M. Williamson, T.A. Miller, J. Chem. Phys. 98 (1993) 2682).

Resolving degeneracy in quadratic programming

A technique for the resolution of degeneracy in an Active Set Method for Quadratic Programming is described. The approach generalises Fletcher's method [2] which applies to the LP case. The method is described in terms of an LCP tableau, which is seen to provide useful insights. It is shown that the degeneracy procedure only needs to operate when the degenerate constraints are linearly dependent on those in the active set. No significant overheads are incurred by the degeneracy procedure. It is readily implemented in a null space format, and no complications in the matrix algebra are introduced.

On degeneracy in linear programming and related problems

Methods related to Wolfe's recursive method for the resolution of degeneracy in linear programming are discussed, and a nonrecursive variant which works with probability one suggested. Numerical results for both nondegenerate problems and problems constructed to have degenerate optima are reported. These are obtained using a careful implementation of the projected gradient algorithm [11]. These are compared with results obtained using a steepest descent approach which can be implemented by means of a closely related projected gradient method, and which is not affected by degeneracy in principle. However, the problem of correctly identifying degenerate active sets occurs with both algorithms. The numerical results favour the more standard projected gradient procedure which resolves the degeneracy explicitly. Extension of both methods to general polyhedral convex function minimization problems is sketched.

ChemInform Abstract: High Resolution Laser Spectroscopy of Asymmetrically Deuterated Cyclopentadienyl Radicals: A Study of Vibronic Degeneracy Resolution and Jahn‐Teller Distortion

AbstractChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 100 leading journals. To access a ChemInform Abstract of an article which was published elsewhere, please select a “Full Text” option. The original article is trackable via the “References” option.

High resolution laser spectroscopy of asymmetrically deuterated cyclopentadienyl radicals: A study of vibronic degeneracy resolution and Jahn–Teller distortion

The rotationally resolved, laser induced fluorescence, excitation spectra of the partially deuterated cyclopentadienyl radicals, C5H4D and C5HD4, have been observed at low temperature in a supersonic free jet expansion. The observed electronic transition in the uv region corresponds to the à 2A″2■X̃ 2E″1 transition in the symmetric cyclopentadienyl isotopomers with D5h symmetry. In the reduced C2v symmetry of the C5HD4 and C5H4D isotopomers, this electronic transition splits into two distinct vibronic bands, separated by about 9 cm−1, which arise from the two vibronic components X̃1 and X̃2 into which the X̃ state is resolved when the symmetry is lowered. In C5H4D the ground X̃1 state has 2A2 symmetry and a permanently distorted, elongated allyl-like structure while the low-lying X̃2 state has 2B2 symmetry and a compressed dienelike structure. The symmetries of the energy levels and the distortions are reversed for the C5HD4 species. A detailed theoretical model is developed to describe the splitting and the rotational structure of the X̃1 and X̃2 states. Application of this model yields a precise value for the alternation of the C–C bond lengths in the distorted structures. This value is shown to be the same as that describing the dynamically pseudorotating, Jahn–Teller distorted structures in the D5h isotopomers. Additionally, the theory explains anomalous values of the observed inertial defects and relates them to physically meaningful quantities for all the isotopomers in both their X̃1 and X̃2 states. Our results are compared to previous experimental work and ab initio calculations on the cyclopentadienyl radical.

On Exponential Asymptotics for Nonseparable Wave Equations I: Complex Geometrical Optics and Connection

Kelley’s Geometrical Optics method opens an efficient approach to the study of waves when the variables in the wave equation cannot be separated. The trajectories of the Hamilton-Jacobi equation are then needed for access to the wave structure. When several disjoint potential wells are present, account of the interaction between them requires consideration of trajectories and tori in complex phase space and of the unfamiliar connectivity of such complex toroids. It is shown how connection theory across wells and barriers can be reformulated in a manner that is simple and flexible and assures the rigorous reliability needed for exponentially precise approximation to functionals of the Hamiltonian operator in several dimensions. To make this difficult and unfamiliar subject more accessible, its discussion is preceded by a simple example of a double well on a strip domain in two dimensions. Parts II and III will apply the results to the quantitative resolution of degeneracy of discrete and continuous spectra, respectively, for genuine partial differential equations.

Resolution of Degeneracy in Transportation Problems

In this note a method is given to find an independent cell for allocation of an infinitesimally small amount (ɛ) in a degenerate solution of a transportation problem. The suggested method of locating the independent cell ensures improvement of the solution or recognition of its optimality, thereby avoiding unnecessary iterations that result in shifting of the ɛ from one independent cell to another.

Resolution of Degeneracy in Transportation Problems

Resolution of Degeneracy in Transportation Problems