One-dimensional Representation Research Articles

Permutation invariant polynomial neural network approach to fitting potential energy surfaces. IV. Coupled diabatic potential energy matrices.

A machine learning method is proposed for representing the elements of diabatic potential energy matrices (PEMs) with high fidelity. This is an extension of the so-called permutation invariant polynomial-neural network (PIP-NN) method for representing adiabatic potential energy surfaces. While for one-dimensional irreducible representations the diagonal elements of a diabatic PEM are invariant under exchange of identical nuclei in a molecular system, the off-diagonal elements require special symmetry consideration, particularly in the presence of a conical intersection. A multiplicative factor is introduced to take into consideration the particular symmetry properties while maintaining the PIP-NN framework. We demonstrate here that the extended PIP-NN approach is accurate in representing diabatic PEMs, as evidenced by small fitting errors and by the reproduction of absorption spectra and product branching ratios in both H2O( ) and NH3( ) non-adiabatic photodissociation.

Angular resolved power spectral density analysis for improving mirror manufacturing.

Ultra-precise diamond turning is the method of choice for manufacturing freeform optics. Analyzing surface errors in different spatial frequency ranges has mainly been performed in a one-dimensional representation of the power spectral density function. However, the advanced machine dynamics at the fabrication of freeform mirrors result in highly anisotropic surfaces with regular ripples in different orientations. To properly analyze the entire surface in the frequency regime, a new way of representing the two-dimensional power spectral density is introduced in this paper. This novel tool is utilized for the evaluation of an example freeform mirror.

Single-Step Traveling-Wave Quantum State Engineering in the Coherent State Representation

We describe a recently introduced single-step traveling-wave quantum state engineering scheme using the one-dimensional coherent-state representation introduced by Janszky. In this representation, the photon number expansion of the output state is derived in a compact formula that is advantageous for numerical optimization. Using this formula, we determine several sets of physically controllable parameters of the scheme yielding various nonclassical target states.

On the characteristic polynomials of multiparameter pencils

In this paper we study the characteristic polynomial of multiparameter pencil z1A1+z2A2+⋯+zsAs. The main theorem states that a unitary representation of a finitely generated group contains a one-dimensional representation if and only if the characteristic polynomial of its generators contains a linear factor. It follows that a two or three dimensional unitary representation of a finitely generated group is irreducible if and only if the characteristic polynomial of the pencil of its generators is irreducible. The result is of kin to the Dedekind and Frobenius theorem on finite group determinant.

A transfer-operator-based relation between Laplace eigenfunctions and zeros of Selberg zeta functions

Over the last few years Pohl (partly jointly with coauthors) has developed dual ‘slow/fast’ transfer operator approaches to automorphic functions, resonances, and Selberg zeta functions for a certain class of hyperbolic surfaces$\unicode[STIX]{x1D6E4}\backslash \mathbb{H}$with cusps and all finite-dimensional unitary representations$\unicode[STIX]{x1D712}$of$\unicode[STIX]{x1D6E4}$. The eigenfunctions with eigenvalue 1 of the fast transfer operators determine the zeros of the Selberg zeta function for$(\unicode[STIX]{x1D6E4},\unicode[STIX]{x1D712})$. Further, if$\unicode[STIX]{x1D6E4}$is cofinite and$\unicode[STIX]{x1D712}$is the trivial one-dimensional representation then highly regular eigenfunctions with eigenvalue 1 of the slow transfer operators characterize Maass cusp forms for$\unicode[STIX]{x1D6E4}$. Conjecturally, this characterization extends to more general automorphic functions as well as to residues at resonances. In this article we study, without relying on Selberg theory, the relation between the eigenspaces of these two types of transfer operators for any Hecke triangle surface$\unicode[STIX]{x1D6E4}\backslash \mathbb{H}$of finite or infinite area and any finite-dimensional unitary representation$\unicode[STIX]{x1D712}$of the Hecke triangle group $\unicode[STIX]{x1D6E4}$. In particular, we provide explicit isomorphisms between relevant subspaces. This solves a conjecture by Möller and Pohl, characterizes some of the zeros of the Selberg zeta functions independently of the Selberg trace formula, and supports the previously mentioned conjectures.

Relative Peripheral Myopia Induced by Fractal Contact Lenses

ABSTRACT Purpose To assess the peripheral refraction induced by Fractal Contact Lenses (FCLs) in myopic eyes by means of a two-dimensional Relative Peripheral Refractive Error (RPRE) map. Materials and Methods This study involved 26 myopic subjects ranging from −0.50 D to −7.00 D. FCLs prototypes were custom-manufactured and characterized. Corneal topographies were taken in order to assess correlations between corneal asphericity and lens decentration. Two-dimensional RPREs were measured with an open-field autorefractor at 67 points, covering the central 60 × 30 degrees of the visual field. The bidimensional RPRE vector components: M, J0 and J45 of the difference between the values obtained with and without the FCLs in the eye were obtained. Additionally, the FCL-induced peripheral refraction in tangential and sagittal planes was computed along the horizontal meridian. Results Induced by the FCLs, significant differences for all vector components were found in the peripheral retina. FCLs were decentered a mean of 0.7 ± 0.19 mm to the temporal cornea. The two-dimensional RPRE maps manifested the FCLs decentration. In particular, M varied asymmetrically between nasal and temporal retina after fitting the FCLs with a significant increment of the myopic shift beyond 10º (p < 0.05). No correlations were found between the amount of lens decentration and the asphericity of the cornea along temporal and nasal sides. However, significant correlations were found between the corneal asphericity and vector components of the RPRE in naked eyes. FCLs produced an increasing myopic shift in tangential and sagittal power errors along the horizontal meridian. Conclusions As predicted by ray-tracing simulations, FCLs fitted in myopic eyes produce a myopic shift of the RPRE. The two-dimensional RPRE maps show information about the lens performance that is hidden in the conventional one-dimensional meridional representations.

Representations of quantum groups at roots of unity, Whittaker vectors and q-W algebras

Let Uε(g) be the standard simply connected version of the Drinfeld–Jumbo quantum group at an odd m-th root of unity ε. The center of Uε(g) contains a huge commutative subalgebra isomorphic to the algebra ZG of regular functions on (a finite covering of a big cell in) a complex connected, simply connected algebraic group G with Lie algebra g. Let V be a finite-dimensional representation of Uε(g) on which ZG acts according to a non-trivial character ηg given by evaluation of regular functions at g∈G. Then V is a representation of the finite-dimensional algebra Uηg=Uε(g)/Uε(g)Kerηg. We show that in this case, under certain restrictions on m, Uηg contains a subalgebra Uηg(m−) of dimension m12dimO, where O is the conjugacy class of g, and Uηg(m−) has a one-dimensional representation Cχg. We also prove that if V is not trivial then the space of Whittaker vectors HomUηg(m−)(Cχg,V) is not trivial and the algebra Wηg=EndUηg(Uηg⊗Uηg(m−)Cχg) naturally acts on it which gives rise to a Schur-type duality between representations of the algebra Uηg and of the algebra Wηg called a q-W algebra.

Torus principal component analysis with applications to RNA structure

There are several cutting edge applications needing PCA methods for data on tori, and we propose a novel torus-PCA method that adaptively favors low-dimensional representations while preventing overfitting by a new test—both of which can be generally applied and address shortcomings in two previously proposed PCA methods. Unlike tangent space PCA, our torus-PCA features structure fidelity by honoring the cyclic topology of the data space and, unlike geodesic PCA, produces nonwinding, nondense descriptors. These features are achieved by deforming tori into spheres with self-gluing and then using a variant of the recently developed principal nested spheres analysis. This PCA analysis involves a step of subsphere fitting, and we provide a new test to avoid overfitting. We validate our torus-PCA by application to an RNA benchmark data set. Further, using a larger RNA data set, torus-PCA recovers previously found structure, now globally at the one-dimensional representation, which is not accessible via tangent space PCA.

On the measurement of voter ideology

We propose a novel measure of voter ideology and study the (socio-economic) determinants of political beliefs. We examine the dimensionality of contemporary voter ideology using survey data of a representative sample of Dutch citizens. Using factor-analyses, we identify and validate four relevant dimensions that capture (1) preferences for economic equality, (2) preferences for markets and efficiency, (3) preferences for personal and cultural freedom, and (4) nationalist, protectionist and populist preferences. We continue with a regression analysis on the determinants of multidimensional voter ideology and compare these to the determinants of the traditional left-right measure of ideology. We find that there is substantial heterogeneity in the determinants of political preferences. Moreover, using a one-dimensional left-right representation of voter ideology conceals most of this heterogeneity.

Magnetic structure of the swedenborgiteCaBa(Co3Fe)O7derived by unpolarized neutron diffraction and spherical neutron polarimetry

We present a study that combines polarized and unpolarized neutrons to derive the magnetic structure of the swedenborgite compound $\mathrm{CaBa}({\mathrm{Co}}_{3}\mathrm{Fe}){\mathrm{O}}_{7}$. Integrated intensities from a standard neutron diffraction experiment and polarization matrices from spherical neutron polarimetry have been simultaneously analyzed revealing a complex order, which differs from the usual spin configurations on a kagome lattice. We find that the magnetic structure is well described by a combination of two one-dimensional representations corresponding to the magnetic superspace symmetry $P{2}_{1}^{\ensuremath{'}}$, and it consists of spins rotating around an axis close to the [110] direction. Due to the propagation vector $\mathbf{q}=(\frac{1}{3}00)$, this modulation has cycloidal and helicoidal character rendering this system a potential multiferroic. The resulting spin configuration can be mapped onto the classical $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ structure of a kagome lattice, and it indicates an important interplay between the kagome and the triangular layers of the crystal structure.

Quantifying matrix product state

Motivated by the concept of quantum finite-state machines, we have investigated their relation with matrix product state of quantum spin systems. Matrix product states play a crucial role in the context of quantum information processing and are considered as a valuable asset for quantum information and communication purpose. It is an effective way to represent states of entangled systems. In this paper, we have designed quantum finite-state machines of one-dimensional matrix product state representations for quantum spin systems.

Orders of torsion units of integral reality-based algebras with rational multiplicities

A reality-based algebra (RBA) is a finite-dimensional associative algebra with involution over [Formula: see text] whose distinguished basis [Formula: see text] contains [Formula: see text] and is closed under pseudo-inverse. An integral RBA is one whose structure constants in its distinguished basis are integers. If the algebra has a one-dimensional representation taking positive values on [Formula: see text], then we say that the RBA has a positive degree map. These RBAs have a standard feasible trace, and the multiplicities of the irreducible characters in the standard feasible trace are the multiplicities of the RBA. In this paper, we show that for integral RBAs with positive degree map whose multiplicities are rational, any finite subgroup of torsion units whose elements are all of degree [Formula: see text] and have algebraic integer coefficients must have order dividing a certain positive integer determined by the degree map and the multiplicities. The paper concludes with a thorough investigation of the properties of RBAs that force multiplicities to be rational.

On Formalization of Information Dissemination Processes Based on Hybrid Diffusion Models

This paper proposes an approach to constructing hybrid mathematical models of dynamics of information dissemination process in a certain social or regional group of population. The proposed technique allows one to describe the levels of influence and storage of information based on the solution of diffusion equation whose variation of propagation intervals is modeled by additional relations in the form of differential equations. A scalar solution for the one-dimensional and two-dimensional representation of contingent is considered.

A Padé Approximate Model of Lithium Ion Batteries

We present a reduced order model for a lithium ion battery in which Padé approximants are used to simplify complex, transcendental, transfer functions associated with the linearized, pseudo 2-dimensional (P2D) electrochemical model of the battery. The resulting transfer functions take the form of simple, rational polynomial functions, which can be used to compute any variable at any location within a one-dimensional representation of the battery domain. Corrections for nonlinear behavior are also incorporated into the reduced model. The results obtained using the reduced model compare favorably to those from the full (nonlinear) P2D model and the computational time required to produce these results is significantly reduced. Importantly, the form of the reduced model means that variables can be evaluated at specific discrete locations within the cell domain, without the need to compute all values of the variable at all discrete locations, as is the case with the spatial discretization methods most commonly used to implement the P2D model. We show that this results in further significant time savings and enhances the suitability of the model for variety of applications.

Terahertz emission from the intrinsic Josephson junctions of high-symmetry thermally-managed Bi2Sr2CaCu2O8+δ microstrip antennas

We show for high-symmetry disk, square, or equilateral triangular thin microstrip antennas of any composition respectively obeying C∞v, C4v, and C3v point group symmetries, that the transverse magnetic electromagnetic cavity mode wave functions are restricted in form to those that are one-dimensional representations of those point groups. Plots of the common nodal points of the ten lowest-energy non-radiating two-dimensional representations of each of these three symmetries are presented. For comparison with symmetry-broken disk intrinsic Josephson junction microstrip antennas constructed from the highly anisotropic layered superconductor Bi2Sr2CaCu2O8+δ (BSCCO), we present plots of the ten lowest frequency orthonormal wave functions and of their emission power angular distributions. These results are compared with previous results for square and equilateral triangular thin microstrip antennas.

Nonlinear dynamic model of Molten-Salt Reactor Experiment – Validation and operational analysis

Several molten-salt reactor (MSR) concepts are currently being developed by private vendors and national organizations. Molten-Salt Reactor Experiment (MSRE) is the only MSR that operated for several years, for which the performance was well documented in the literature. Experimental data from MSRE serve as the standard for developing models and tools for MSR analysis. MSRE underwent several design changes from conception to construction to operation. Model validation requires the use of parameters consistent with those that existed during the various measurements. The paper therefore presents a brief discussion of the parameters that evolved over time, and details of sources for all the parameters used in the modeling. This report is part of a series of papers on modeling MSR dynamics. The goal here is to validate the modeling approach by comparing simulation results with experimental data. For this purpose, two nonlinear dynamic models are developed. The first model uses a one-region one-dimensional representation of the core. The second reproduces the nine-region core model developed by Oak Ridge National Laboratory for MSRE studies. The dynamics are analyzed by simulating transients during normal power operation. The frequency response of the models is also evaluated. Both models show excellent agreement with experimental data for both U-235 and U-233 fuels. Some apparent discrepancies in experimental data are reported and their consequences discussed. The one-region model is modified to simulate reactivity excursions resulting from operational anomalies, and the results are presented. This modeling approach can be applied to other MSR systems provided valid system parameters.

Impact of paper and wooden collections on humidity stability and energy consumption in museums and libraries

Much research has been focused on maintaining stable humidity conditions in buildings housing heritage collections while reducing energy use. Moisture buffering by collections themselves can have a marked effect on the stabilisation of relative humidity (RH), the key parameter for preservation. Modelling of moisture transport using COMSOL Multiphysics was applied to transform three-dimensional paper and wooden objects into their one-dimensional representations, without changing the moisture uptake and release characteristics. The results were coupled to the modelling of indoor microclimate and energy consumption in collection storage spaces with the use of WUFI®Plus software. The study revealed the crucial impact of air exchange rate of the building on the stability of indoor RH and the humidification and dehumidification loads required to maintain it. In the adequately air-tight library store, a sizeable paper collection was found to reduce the RH fluctuations from ±9% to ±6% around the yearly average and the energy consumption due to the humidification and dehumidification load by 38% when compared with the empty space, for a high-quality climate control scenario. In turn, a wooden collection, occupying a realistic fraction of a museum store was not large enough to significantly narrow down the RH variations and reduce the energy consumption.

Micro-sphere based viscoplastic constitutive model for uncured green rubber

Uncured rubber exhibits strong viscoplastic flow without a distinct yield point accompanied by hardening. Classical hyperelastic models developed for crosslinked rubber do not apply to uncured rubber due to the lack of crosslinks which endow the material its elasticity. This paper presents a new constitutive model for the isothermal response of uncured green rubber. The kinematic structure of the proposed approach is based on the affine micro-sphere model. The computation of the stretch in the orientation direction follows the Cauchy-Born rule. The micro-sphere enables numerical integration over the unit sphere via finite summation over the orientation directions corresponding to the integration points over the sphere. This structure replaces the complex three-dimensional formulations of finite inelasticity based on the multiplicative split of the deformation gradient by a simpler and more attractive one-dimensional rheological representation at the orientation directions. The rheology of the model consists of two parts: (i) a part responsible for the rate-independent reponse and (ii) a part responsible for the rate-dependent response, respectively. The first branch consists of a spring connected to a modified Kelvin element, where the latter spring models the kinematic hardening. The dashpot describes a time-independent endochronic flow rule based solely on the deformation history. The second branch consists of a spring connected to a Maxwell element in parallel to a dashpot. The two dashpots in the latter branch model the ground-state viscoelasticity and rate-dependent hardening phenomenon. Albeit its apparent complexity, the proposed rheology and its numerical implementation are straightforward. The proposed model shows favorable results suitable for large scale finite element based simulations for forming process of uncured rubber components.

Motif Discovery in Speech: Application to Monitoring Alzheimer's Disease.

Perseveration - repetition of words, phrases or questions in speech - is commonly described in Alzheimer's disease (AD). Measuring perseveration is difficult, but may index cognitive performance, aiding diagnosis and disease monitoring. Continuous recording of speech would produce a large quantity of data requiring painstaking manual analysis, and risk violating patients' and others' privacy. A secure record and an automated approach to analysis are required. To record bone-conducted acoustic energy fluctuations from a subject's vocal apparatus using an accelerometer, to describe the recording and analysis stages in detail, and demonstrate that the approach is feasible in AD. Speech-related vibration was captured by an accelerometer, affixed above the temporomandibular joint. Healthy subjects read a script with embedded repetitions. Features were extracted from recorded signals and combined using Principal Component Analysis to obtain a one-dimensional representation of the feature vector. Motif discovery techniques were used to detect repeated segments. The equipment was tested in AD patients to determine device acceptability and recording quality. Comparison with the known location of embedded motifs suggests that, with appropriate parameter tuning, the motif discovery method can detect repetitions. The device was acceptable to patients and produced adequate signal quality in their home environments. We established that continuously recording bone-conducted speech and detecting perseverative patterns were both possible. In future studies we plan to associate the frequency of verbal repetitions with stage, progression and type of dementia. It is possible that the method could contribute to the assessment of disease-modifying treatments.

Attitudes towards science among Spanish citizens: The case of critical engagers.

Using data obtained from Spanish surveys on the public perception of science, this article presents a critical review of current practices of population profile segmentation, including the one-dimensional representation of perceived risks and benefits and of the systematic underestimation of critical attitudes to the social impact of science and technology. We use discriminant analysis to detect a somewhat hidden cluster in the Spanish population which we call 'critical engagers'. These individuals are critically and socially responsible and are not reticent about expressing concern regarding scientific-technological change. While they hold an overall positive attitude towards change of this kind, they are at the same time well aware of the risks posed by particular fields of application. We highlight the academic interest and political value of these individuals, attributing to this population a mature and intelligent stance which may well be employed in enhancing the relationship between science and society.