Unfolding Problem Research Articles

Chameleon: a cloud computing Industry 4.0 neutron spectrum unfolding code.

This work presents Chameleon, a cloud computing (CC) Industry 4.0 (I4) neutron spectrum unfolding code. The code was designed under the Python programming language, using Streamlit framework®, and it is executed on the cloud, as I4 CC technology through internet, by using mobile devices with internet connectivity and a web navigator. In its first version, as a proof of concept, the SPUNIT algorithm was implemented. The main functionalities and the preliminary tests performed to validate the code are presented. Chameleon solves the neutron spectrum unfolding problem and it is easy, friendly and intuitive. It can be applied with success in various workplaces. More validation tests are in progress. Future implementations will include improving the graphical user interface, inserting other algorithms, such as GRAVEL, MAXED and neural networks, and implementing an algorithm to estimate uncertainties in the calculated integral quantities.

Regularised unfolding with a discrete-valued penalty function

Regularisation allows one to handle ill-posed inverse problems. Here we focus on discrete unfolding problems. The properties of the results are characterised by the consistency between measurements and unfolding result and by the posterior response matrix. We introduce a novel regularisation scheme based on a discrete-valued penalty function and compare its performance to that of a simple cutoff-regularisation. The discrete-valued penalty function does not require a regularisation parameter that needs to be adjusted on a case-by-case basis. In toy studies very satisfactory results are obtained.

Autoencoder-extended Conditional Invertible Neural Networks for Unfolding Signal Traces

The reconstruction of cosmic ray-induced air showers from measurements of radio waves constitutes a major challenge. In this work, we focus on recovering the full three-dimensional electromagnetic field from two recorded signal traces of an antenna station covering two horizontal polarization directions. The simulated field is folded by a direction and frequency-dependent characteristic antenna response pattern, resulting in voltage signal traces as a function of time. Both signal traces are contaminated by simulated background noise. We use conditional Invertible Neural Networks (cINNs) to learn posterior distributions, from which the most likely electromagnetic field given a measured signal trace can be inferred. To improve robustness, we extend the method with an autoencoder by reducing the parameter phase space and decoupling the cINN from specific data shapes. Thereby, each signal trace is condensed into a small number of abstract parameters in the latent space on which the cINN operates. The presented method shows promising results and can be transferred to other unfolding problems where the recovery of the pre-measurement state is of interest.

Uncertainty quantification for wide-bin unfolding: one-at-a-time strict bounds and prior-optimized confidence intervals

Unfolding is an ill-posed inverse problem in particle physics aiming to infer a true particle-level spectrum from smeared detector-level data. For computational and practical reasons, these spaces are typically discretized using histograms, and the smearing is modeled through a response matrix corresponding to a discretized smearing kernel of the particle detector. This response matrix depends on the unknown shape of the true spectrum, leading to a fundamental systematic uncertainty in the unfolding problem. To handle the ill-posed nature of the problem, common approaches regularize the problem either directly via methods such as Tikhonov regularization, or implicitly by using wide-bins in the true space that match the resolution of the detector. Unfortunately, both of these methods lead to a non-trivial bias in the unfolded estimator, thereby hampering frequentist coverage guarantees for confidence intervals constructed from these methods. We propose two new approaches to addressing the bias in the wide-bin setting through methods called One-at-a-time Strict Bounds (OSB) and Prior-Optimized (PO) intervals. The OSB intervals are a bin-wise modification of an existing guaranteed-coverage procedure, while the PO intervals are based on a decision-theoretic view of the problem. Importantly, both approaches provide well-calibrated frequentist confidence intervals even in constrained and rank-deficient settings. These methods are built upon a more general answer to the wide-bin bias problem, involving unfolding with fine bins first, followed by constructing confidence intervals for linear functionals of the fine-bin counts. We test and compare these methods to other available methodologies in a wide-bin deconvolution example and a realistic particle physics simulation of unfolding a steeply falling particle spectrum.

Post-hoc regularisation of unfolded cross-section measurements

Neutrino cross-section measurements are often presented as unfolded binned distributions in “true” variables. The ill-posedness of the unfolding problem can lead to results with strong anti-correlations and fluctuations between bins, which make comparisons to theoretical models in plots difficult. To alleviate this problem, one can introduce regularisation terms in the unfolding procedure. These suppress the anti-correlations in the result, at the cost of introducing some bias towards the expected shape of the data.This paper discusses a method using simple linear algebra, which makes it is possible to regularise any result that is presented as a central value and a covariance matrix. This “post-hoc” regularisation is generally much faster than repeating the unfolding method with different regularisation terms. The method also yields a regularisation matrix which connects the regularised to the unregularised result, and can be used to retain the full statistical power of the unregularised result when publishing a nicer looking regularised result.In addition to the regularisation method, this paper also presents some thoughts on the presentation of correlated data in general. When using the proposed method, the bias of the regularisation can be understood as a data visualisation problem rather than a statistical one. The strength of the regularisation can be chosen by minimising the difference between the implicitly uncorrelated distribution shown in the plots and the actual distribution described by the unregularised central value and covariance.Aside from minimising the difference between the shown and the actual result, additional information can be provided by showing the local log-likelihood gradient of the models shown in the plots. This adds more information about where the model is “pulled” by the data than just comparing the bin values to the data's central values.

From an Old Problem to a New Solution: Identity and Ideology in The Egg and the Chicken by Clarice Lispector

This paper analyzes the short story The Egg and the Chicken by Clarice Lispector by examining the issues of identity, ideology and gender. The selected text is one of the outstanding works by this increasingly well-regarded Brazilian author and reappraises the age-old question of which came first: the chicken or the egg. The short story is explicitly concerned with its own dialectical language and the attempt to open up new philosophical perspectives on the long-standing boundaries of this issue through a discussion of the concept of origins and its deconstruction. The formal language employed in the short story seems somewhat contradictory in its effect, primarily due to its syntactic and stylistic simplicity and clarity via short, informative sentences and simple tenses to break down the given mental images. However, the story is notable for obscuring the content, invoking semantic and philosophical engagement by utilizing paradoxical and dialectical expressions. The chicken-egg paradox is both a quotidian metaphor and a multi-dimensional problem that exists on numerous levels. This paper, therefore, examines the language of the short story and seeks to find the answer/s to the dilemma. Unlike the general conception of the problem as an eternal issue or chicken-precedence, this research concludes that Lispector’s work re-addresses and problematizes this age-old question by unfolding several other potential problems or challenges within the paradox by placing a particular focus on the aspects of identity, ideology and gender

Study on iterative regularization method and application to neutron spectrum unfolding of multi-sphere spectrometer measurement

An iterative regularization method combining the Lanczos bidiagonalization with Tikhonov regularization is proposed and applied to neutron spectrum unfolding of a newly-developed compact multi-sphere spectrometer. The unfolding is processed as a determined problem without any prior information, which is different from the traditional way. Comparison study of the two commonly-used unfolding methods, GRAVEL and MLEM with the iterative regularization method is carried out. The “semi-convergence” behavior appears for readings containing large uncertainties with the GRAVEL and MLEM methods, making the unfolded spectrums deviate from the true solutions. However, there is no semi-convergence behavior appearing with the iterative regularization method. The unfolded spectrums get close to the true solution as the number of iterations grows. Experimental measurement is carried out for measuring neutron spectrum of 241 Am–Be neutron source using the compact multi-sphere spectrometer. The measured data are also unfolded. Compared with the ISO reference spectrum, the unfolded results with GRAVEL and MLEM methods deviate from the reference spectrum due to the semi-convergence behavior, while the unfolded spectrum with the iterative regularization method agrees well with the reference spectrum, indicating that the iterative regularization method is adaptable to unfolding problems with both accurate measured readings and measured readings with large uncertainties.

Comparison of unfolding methods using RooFitUnfold

In this paper we describe RooFitUnfold, an extension of the RooFit statistical software package to treat unfolding problems, and which includes most of the unfolding methods that commonly used in particle physics. The package provides a common interface to these algorithms as well as common uniform methods to evaluate their performance in terms of bias, variance and coverage. In this paper we exploit this common interface of RooFitUnfold to compare the performance of unfolding with the Richardson–Lucy, Iterative Dynamically Stabilized, Tikhonov, Gaussian Process, bin-by-bin and inversion methods on several example problems.

A Primal-dual algorithm for unfolding neutron energy spectrum from multiple activation foils

In this paper we propose a robust and efficient primal-dual interior-point method for a nonlinear ill-conditioned problem with associated errors which are arising in the unfolding procedure for neutron energy spectrum from multiple activation foils. Based on the maximum entropy principle and Boltzmann's entropy formula, the discrete form of the unfolding problem is equivalent to computing the analytic center of the polyhedral set \begin{document}$ P = \{x \in R^n \mid Ax = b, x \ge 0\} $\end{document} , where the matrix \begin{document}$ A \in R^{m\times n} $\end{document} is ill-conditioned, and both \begin{document}$ A $\end{document} and \begin{document}$ b $\end{document} are inaccurate. By some derivations, we find a new regularization method to reformulate the problem into a well-conditioned problem which can also reduce the impact of errors in \begin{document}$ A $\end{document} and \begin{document}$ b $\end{document} . Then based on the primal-dual interior-point methods for linear programming, we propose a hybrid algorithm for this ill-conditioned problem with errors. Numerical results on a set of ill-conditioned problems for academic purposes and two practical data sets for unfolding the neutron energy spectrum are presented to demonstrate the effectiveness and robustness of the proposed method.

A Hierarchical Bayesian Approach to Neutron Spectrum Unfolding With Organic Scintillators

We propose a hierarchical Bayesian model and a state-of-the-art Monte Carlo sampling method to solve the unfolding problem, i.e., to estimate the spectrum of an unknown neutron source from the data detected by an organic scintillator. Inferring neutron spectra is important for several applications, including nonproliferation and nuclear security, as it allows the discrimination of fission sources in special nuclear material (SNM) from other types of neutron sources based on the differences of the emitted neutron spectra. Organic scintillators interact with neutrons mostly via elastic scattering on hydrogen nuclei and therefore partially retain neutron energy information. Consequently, the neutron spectrum can be derived through deconvolution of the measured light-output spectrum and the response functions of the scintillator to monoenergetic neutrons. The proposed approach is compared to three existing methods using the simulated data to enable controlled benchmarks. We consider three sets of detector responses. One set corresponds to a 2.5-MeV monoenergetic neutron source and two sets are associated with (energywise) continuous neutron sources ( <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">252</sup> Cf and <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">241</sup> AmBe). Our results show that the proposed method has similar or better unfolding performance compared with other iterative or Tikhonov regularization-based approaches in terms of accuracy and robustness against limited detection events while requiring less user supervision. The proposed method also provides a posteriori confidence measures, which offers additional information regarding the uncertainty of the measurements and the extracted information.

Neutron spectrum unfolding of the multiple activation foils based on sparse representation

An unfolding method based on sparse representation is proposed and applied to unfolding problem of multiple activation foils measurement. The Online Dictionary Learning (ODL) algorithm is applied for sparse representation. The algorithm LARS-EN is used for reconstruction. The Akaike’s Information Criterion (AIC) is applied to select the best coefficient path. Nuclear reactor of Qinshan phase II nuclear power plant (NPP) is considered as the study object and training samples are generated by Monte Carlo code MCNP. By using the unfolding method proposed in this paper, two sets of neutron spectrums are unfolded successfully with acceptable accuracies. The first set contains 4 neutron spectrums of different shapes; and the second set contains 4 neutron spectrums at different positions of the radiation surveillance capsule. Moreover, neutron spectrums of the radiation surveillance capsule can also be unfolded with acceptable accuracies with fewer equations while the two fission detectors 238U and 237Np are removed.

Multidimensional unfolding problem solution in the case of a single target

Multidimensional unfolding (statistical deployment, prefscal) is the method for placing simultaneously on the same map a set of observers and a set of targets with fixed distances between each observer and each of the targets. The approximate methods of solving it today suggest that in each of these sets there has at least two elements. In this paper, we propose a method for the exact solution of this problem, when the set of targets is a singleton. Algorithms are easily transferred to the case of only one observer.

An application of genetic multi-objective optimization algorithm to neutron spectrum unfolding problem

An application of genetic multi-objective optimization algorithm to neutron spectrum unfolding problem

Emotional Sound Symbolism and the Volta in Shakespearean and Petrarchan Sonnets

Sonnets written in the Shakespearean or Petrarchan form are both assumed to present and then answer a problem, but they do so in different ways. The two forms have different rhyming schemes. The volta or turn is predicted to occur between lines 12 and 13 in the first and lines 8 and 9 in the second form. It is argued that sound in poetry is emotionally communicative (symbolic), especially when the predominance of Harsh (e.g., t, r) over Gentle (e.g., l, m) sounds is considered. An analysis of the sounds (phonemes) in various exemplars of the two forms (N=285 sonnets) was undertaken. Shakespeare’s sonnets represented his form and those of a variety of authors represented the Petrarchan form. Predominant Harshness was the dependent variable in a design which compared line and form. There were significant effects associated with line, form, and their interaction (p&lt;.05). Shakespeare’s sonnets, had a lower predominant Harshness than the Petrarchan sonnets. Both Shakespearean and Petrarchan sonnets exhibited a major drop in predominant Harshness (a volta) between lines 8 and 9. Both began on a gentle note, increased in predominant Harshness as problems were being expounded, and returned to a gentler note for their endings. Only Shakespearean sonnets had a spike in harshness in the third quatrain, suggesting that the author was still unfolding problems rather than resolving them there.

Mechanism and structural diversity of exoribonuclease-resistant RNA structures in flaviviral RNAs

Flaviviruses such as Yellow fever, Dengue, West Nile, and Zika generate disease-linked viral noncoding RNAs called subgenomic flavivirus RNAs. Subgenomic flavivirus RNAs result when the 5′–3′ progression of cellular exoribonuclease Xrn1 is blocked by RNA elements called Xrn1-resistant RNAs located within the viral genome’s 3′-untranslated region that operate without protein co-factors. Here, we show that Xrn1-resistant RNAs can halt diverse exoribonucleases, revealing a mechanism in which they act as general mechanical blocks that ‘brace’ against an enzyme’s surface, presenting an unfolding problem that confounds further enzyme progression. Further, we directly demonstrate that Xrn1-resistant RNAs exist in a diverse set of flaviviruses, including some specific to insects or with no known arthropod vector. These Xrn1-resistant RNAs comprise two secondary structural classes that mirror previously reported phylogenic analysis. Our discoveries have implications for the evolution of exoribonuclease resistance, the use of Xrn1-resistant RNAs in synthetic biology, and the development of new therapies.

Shape-constrained uncertainty quantification in unfolding steeply falling elementary particle spectra

The high energy physics unfolding problem is an important statistical inverse problem in data analysis at the Large Hadron Collider (LHC) at CERN. The goal of unfolding is to make nonparametric inferences about a particle spectrum from measurements smeared by the finite resolution of the particle detectors. Previous unfolding methods use ad hoc discretization and regularization, resulting in confidence intervals that can have significantly lower coverage than their nominal level. Instead of regularizing using a roughness penalty or stopping iterative methods early, we impose physically motivated shape constraints: positivity, monotonicity, and convexity. We quantify the uncertainty by constructing a nonparametric confidence set for the true spectrum, consisting of all those spectra that satisfy the shape constraints and that predict the observations within an appropriately calibrated level of fit. Projecting that set produces simultaneous confidence intervals for all functionals of the spectrum, including averages within bins. The confidence intervals have guaranteed conservative frequentist finite-sample coverage in the important and challenging class of unfolding problems for steeply falling particle spectra. We demonstrate the method using simulations that mimic unfolding the inclusive jet transverse momentum spectrum at the LHC. The shape-constrained intervals provide usefully tight conservative inferences, while the conventional methods suffer from severe undercoverage.

Potential reduction interior point algorithm unfolding of neutron energy spectrum measured by recoil proton method**supported by Fundamental Research Funds for Central Universities (2016XS61), and Opening Foundation of State Key Laboratory of Intense Pulsed Radiation Simulation and Effect.

A reconstruction algorithm for unfolding neutron energy spectra has been developed, based for the first time on the potential reduction interior point algorithm. This algorithm can be easily applied to neutron energy spectrum reconstruction in the recoil proton method. We transform the neutron energy spectrum unfolding problem into a typical nonnegative linear complementarity problem. The recoil proton energy spectrum and response matrix at angles of 0° and 30° are generated by the Geant4 simulation toolkit. Several different neutron energy test spectra are also employed. It is found that this unfolding algorithm is stable and provides efficient, accurate results.

Warhead verification as inverse problem: Applications of neutron spectrum unfolding from organic-scintillator measurements

Verification of future warhead-dismantlement treaties will require detection of certain warhead attributes without the disclosure of sensitive design information, and this presents an unusual measurement challenge. Neutron spectroscopy—commonly eschewed as an ill-posed inverse problem—may hold special advantages for warhead verification by virtue of its insensitivity to certain neutron-source parameters like plutonium isotopics. In this article, we investigate the usefulness of unfolded neutron spectra obtained from organic-scintillator data for verifying a particular treaty-relevant warhead attribute: the presence of high-explosive and neutron-reflecting materials. Toward this end, several improvements on current unfolding capabilities are demonstrated: deuterated detectors are shown to have superior response-matrix condition to that of standard hydrogen-base scintintillators; a novel data-discretization scheme is proposed which removes important detector nonlinearities; and a technique is described for re-parameterizing the unfolding problem in order to constrain the parameter space of solutions sought, sidestepping the inverse problem altogether. These improvements are demonstrated with trial measurements and verified using accelerator-based time-of-flight calculation of reference spectra. Then, a demonstration is presented in which the elemental compositions of low-Z neutron-attenuating materials are estimated to within 10%. These techniques could have direct application in verifying the presence of high-explosive materials in a neutron-emitting test item, as well as other for treaty verification challenges.

Computing Average Passive Forces in Sarcomeres in Length-Ramp Simulations.

Passive forces in sarcomeres are mainly related to the giant protein titin. Titin’s extensible region consists of spring-like elements acting in series. In skeletal muscles these elements are the PEVK segment, two distinct immunoglobulin (Ig) domain regions (proximal and distal), and a N2A portion. While distal Ig domains are thought to form inextensible end filaments in intact sarcomeres, proximal Ig domains unfold in a force- and time-dependent manner. In length-ramp experiments of single titin strands, sequential unfolding of Ig domains leads to a typical saw-tooth pattern in force-elongation curves which can be simulated by Monte Carlo simulations. In sarcomeres, where more than a thousand titin strands are arranged in parallel, numerous Monte Carlo simulations are required to estimate the resultant force of all titin filaments based on the non-uniform titin elongations. To simplify calculations, the stochastic model of passive forces is often replaced by linear or non-linear deterministic and phenomenological functions. However, new theories of muscle contraction are based on the hypothesized binding of titin to the actin filament upon activation, and thereby on a prominent role of the structural properties of titin. Therefore, these theories necessitate a detailed analysis of titin forces in length-ramp experiments. In our study we present a simple and efficient alternative to Monte Carlo simulations. Based on a structural titin model, we calculate the exact probability distributions of unfolded Ig domains under length-ramp conditions needed for rigorous analysis of expected forces, distribution of unfolding forces, etc. Due to the generality of our model, the approach is applicable to a wide range of stochastic protein unfolding problems.

Organizational responsiveness: The case of unfolding crises and problem detection within HELCOM

How and to what extent do international organizations detect, process and react to different types of change within their policy domains? This study addresses this question by combining a unique data set consisting of policy documents from the Helsinki Commission (HELCOM) with data measuring ecosystem change in the Baltic Sea during the period 1980–2013. Here HELCOM's responses to two types of ecosystem changes are investigated: fast and visible (summer algae blooms) and slow and opaque (anoxic areas). Finally, this study assesses if the organizational reform of 2007, which introduced the ecosystem approach, has had any effects on HELCOM responsiveness. It is found that HELCOM, contrary to expectations, is only responding systematically to slow-moving and opaque processes but that this response confirms the anticipated organizational bottom-up pattern. The ecosystem approach reform seems to have had a negative effect on the responsiveness of HELCOM; however, a general trend is that HELCOM over time has become more responsive in the lower levels of the organization. The lack of an immediate effect regarding the ecosystem approach reform can serve as a reminder of the absence of panaceas in policy making in general, and in environmental governance in particular.