Miracle-dz/UniFAR-FTUs huggingface dataset:
Signatures of symmetry and electronic structure in high-order harmonic generation in polyatomic molecules

We report detailed measurements of high-order harmonic generation in chloromethane molecules (CCl{sub 4}, CHCl{sub 3}, and CH{sub 2}Cl{sub 2}) to show that fingerprints of symmetry and electronic structure can be decoded from high-order harmonic generation even in complex randomly oriented molecules. In our measurements, orbital symmetries of these molecules are manifested as both extended harmonic cutoffs and a local minimum in the ellipticity dependence of the cut-off harmonics, suggesting the occurrence of quantum interferences during ionization. The harmonic spectra exhibit distinct interference minima at {approx}42 and {approx}60 eV. We attribute the former to the Cooper minimum in the photoionization cross section and the latter to intramolecular interference during the recombination process.
Artin’s criteria for algebraicity revisited

Using notions of homogeneity, as developed in (Hal12b), we give new proofs of M. Artin's algebraicity criteria for functors (Art69b, Thm. 5.3) and groupoids (Art74, Thm. 5.3). Our methods give a more general result, unifying Artin's two theorems and clarifying their dierences. In positive char- acteristic, we also identify a subtle issue in Artin's algebraicity criterion for stacks. With the techniques that we develop, this problem is circumvented.
Effective results for discriminant equations over finitely generated domains

Let $A$ be an integral domain with quotient field $K$ of characteristic $0$ that is finitely generated as a $\mathbb{Z}$-algebra. Denote by $D(F)$ the discriminant of a polynomial $F\in A[X]$. Further, given a finite etale algebra $\Omega$, we denote by $D_{\Omega/K}(\alpha )$ the discriminant of $\alpha$ over $K$. For non-zero $\delta\in A$, we consider equations \[ D(F)=\delta \] to be solved in monic polynomials $F\in A[X]$ of given degree $n\geq 2$ having their zeros in a given finite extension field $G$ of $K$, and \[ D_{\Omega/K}(\alpha)=\delta\,\,\mbox{ in } \alpha\in O, \] where $O$ is an $A$-order of $\Omega$, i.e., a subring of the integral closure of $A$ in $\Omega$ that contains $A$ as well as a $K$-basis of $\Omega$. In our book ``Discriminant Equations in Diophantine Number Theory, which will be published by Cambridge University Press we proved that if $A$ is effectively given in a well-defined sense and integrally closed, then up to natural notions of equivalence the above equations have only finitely many solutions, and that moreover, a full system of representatives for the equivalence classes can be determined effectively. In the present paper, we extend these results to integral domains $A$ that are not necessarily integrally closed.
The Impact of Social Media on Consumer Behavior: The Case of Consumer-Generated Content on YouTube

This research examines the mechanism through which YouTube-based consumer-generated content (CGC) shape consumers’ CGC adoption and subsequent purchase intention. Drawing on the Elaboration Likelihood Model, a causal model is developed to predict the impact of YouTube-based CGC attributes/cues (i.e., information quality, source credibility, and CGC credibility) on perceived usefulness, attitudes toward CGCs, CGC adoption, and, ultimately, purchase intention. A sample of 204 Vietnamese consumers is used to test the hypotheses. The results show that the central cue (i.e. information quality) and peripheral cues (i.e., source credibility and CGC credibility) can predict the changes in perceived usefulness and attitudes toward CGCs, which in turn have an impact on CGC adoption and ultimately the purchase intention of consumers. This study contributes to the CGC literature and the ﬁndings suggest that managers should pay attention to both the central and peripheral cues of YouTube-based CGCs to enhance the eﬀectiveness of marketing strategies.
A New Factor from E6-Mod to E7-Mod

We find a new representation of the simple Lie algebra of type E7 on the polynomial algebra in 27 variables, which gives a fractional representation of the corresponding Lie group on 27-dimensional space. Using this representation and Shen’s idea of mixed product, we construct a functor from E6-Mod to E7-Mod. A condition for the functor to map a finite-dimensional irreducible E6-module to an infinitedimensional irreducible E7-module is obtained. Our general frame also gives a direct polynomial extension from irreducible E6-modules to irreducible E7-modules. The obtained infinite-dimensional irreducible E7-modules are (G,K)-modules in terms of Lie group representations. The results could be used in studying the quantum field theory with E7 symmetry and symmetry of partial differential equations.
Finding any given 2‐factor in sparse pseudorandom graphs efficiently

Given an n ‐vertex pseudorandom graph G and an n ‐vertex graph H with maximum degree at most two, we wish to find a copy of H in G , that is, an embedding φ:V(H)→V(G) so that φ(u)φ(v)∈E(G) for all uv∈E(H) . Particular instances of this problem include finding a triangle‐factor and finding a Hamilton cycle in G . Here, we provide a deterministic polynomial time algorithm that finds a given H in any suitably pseudorandom graph G . The pseudorandom graphs we consider are (p,λ) ‐bijumbled graphs of minimum degree which is a constant proportion of the average degree, that is, Ω(pn) . A (p,λ) ‐bijumbled graph is characterised through the discrepancy property: |e(A,B)−p|A||B||
Tropical Combinatorics and Whittaker functions

We establish a fundamental connection between the geometric RSK correspondence and GL(N,R)-Whittaker functions, analogous to the well known relationship between the RSK correspondence and Schur functions. This gives rise to a natural family of measures associated with GL(N,R)-Whittaker functions which are the analogues in this setting of the Schur measures on integer partitions. The corresponding analogue of the Cauchy-Littlewood identity can be seen as a generalisation of an integral identity for GL(N,R)-Whittaker functions due to Bump and Stade. As an application, we obtain an explicit integral formula for the Laplace transform of the law of the partition function associated with a one-dimensional directed polymer model with log-gamma weights recently introduced by one of the authors (TS).
Relationships between Doppler Spectral Moments within Large-Scale Cirro- and Altostratus Cloud Fields Observed by a Ground-Based 95-GHz Cloud Radar

Abstract In this study, data obtained from measurements with a ground-based vertical-pointing 95-GHz polarimetric cloud radar are analyzed. The investigations concentrate on the relationships between the Doppler spectral moments observed in different regions of nonprecipitating cirrostratus and altostratus decks connected with warm fronts approaching the radar site. In some of these cases, a remarkably well-defined relationship between the radar reflectivity and the spectral width is found. It is demonstrated how this relationship can be used to obtain information on the size distributions and the fallspeeds of the particles in the investigated cloud sections. It is found that if single parameters of the size distributions, for example, are parameterized by a lognormal distribution, they cannot be determined with an acceptable accuracy. However, at least the changes of these parameters, such as mean particle diameter and particle concentration, with changing reflectivity as well as the behavior of the cor.
Stationary behaviour of observables after a quantum quench in the spin-1/2 Heisenberg XXZ chain

We consider a quantum quench in the spin-1/2 Heisenberg XXZ chain. At late times after the quench it is believed that the expectation values of local operators approach time-independent values that are described by a generalized Gibbs ensemble. Employing a quantum transfer matrix approach we show how to determine short-range correlation functions in such generalized Gibbs ensembles for a class of initial states.
Hypergraph expanders of all uniformities from Cayley graphs

Hypergraph expanders are hypergraphs with surprising, non‐intuitive expansion properties. In a recent paper, the first author gave a simple construction, which can be randomized, of 3‐uniform hypergraph expanders with polylogarithmic degree. We generalize this construction, giving a simple construction of r ‐uniform hypergraph expanders for all r⩾3 .
Continuous and Reversible Change of the Magnetic Coupling in an Fe/Nb Multilayer Induced by Hydrogen Charging

We show in this Letter that the magnetic coupling of a [26{Angstrom}Fe/15{Angstrom}Nb]{times}18 multilayer is changed in a continuous and reversible way by introducing hydrogen into the sample. The magnetic structure and its change during hydrogen charging (and the following decharging) is measured {ital in situ} by neutron reflectivity. The alteration of the magnetic coupling upon hydrogenation is confirmed by SQUID magnetization measurements. We attribute the change of the coupling to a change of the effective Fermi wave vector in Nb due to hydrogen uptake. {copyright} {ital 1997} {ital The American Physical Society}
Spectral moment estimation by means of level crossings

Three types of estimator of the second spectral moment of a stationary Gaussian process are considered. The integral estimator is based on the integral of the squared derivative of the process, while crossing estimators make use of the number of upcrossings of zero or nonzero levels. It is shown that the zero-crossing estimator can often compete with the integral estimator in efficiency and that it can be considerably improved by the additional use of nonzero levels.
Optical absorption spectra of intermediate-size silver clusters from first principles

Optical absorption spectra of the three lowest-energy isomers of ${\text{Ag}}_{n}$ $(n=10,12\char21{}20)$ are investigated from first principles within the time-dependent local-density approximation (TDLDA). The computed spectra are found to be generally in good agreement with the available experimental data. The analyses of the spectra indicate that the $d$ electrons of ${\text{Ag}}_{n}$ clusters in this size range have a significant $(70%\char21{}80%)$ contribution to low-energy optical excitations. We show that most of the peak positions and the relative intensities in the TDLDA spectra of these subnanometer sized clusters can be explained remarkably well within the classical Mie-Gans theory, using the dielectric function of bulk Ag and taking into account the shapes of the isomers.
Iterative Mechanisms for Electricity Markets

In order to deal with market power that sporadically results from contingencies (e.g., severe weather, plant outages) most electricity markets have institutions in charge of monitoring market performance and mitigating market power. The latter task is often achieved by producing estimates of marginal costs (also referred to as "reference levels") that may replace the actual bids by generators with market power. In this paper, we propose an iterative mechanism that constitutes an alternative to outright regulatory intervention in those sporadic situations in which market power is a significant concern. The iterative mechanism proposed is based upon relatively simple information exchange between the market maker and market participants and is equipped to handle general non-linear (convex) constraints related to technical and/or reliability requirements. We show the mechanism proposed has many desirable properties (approximately): incentive compatibility, efficiency, individual rationality and (weak) budget balance. In addition, we show it is robust to imperfect information regarding costs. To illustrate we consider its application to the joint clearing of day ahead dispatch and reserves, an approach that has been proposed for the large-scale integration of renewable generation. In this context, we relax the assumption that each generator has perfect information on its own expected marginal costs of adjustment and show the mechanism retains most of its properties.
Rabinowitz-Floer homology on Brieskorn manifolds

This thesis considers fillable contact structures on odd-dimensional manifolds. For that purpose, Rabinowitz-Floer homology (RFH) is used which was introduced by Cieliebak and Frauenfelder in 2009. A major part of the thesis is devoted to technical problems in the definition of RFH. In particular, it is shown that the moduli spaces involved are cut out transversally. Moreover, it is proved that RFH is essentially invariant under subcritical handle attachment. Finally, RFH is calculated for some Brieskorn manifolds. The obtained results are then used to show for every manifold, which supports fillable contact structures, that there exist either infinitely many different fillable contact structures, or one contact structure with infinitely many different fillings or for every fillable contact structure holds that RFH is infinite dimensional in every degree.
Higgs Amplitudes From Twistor Inspired Methods

We illustrate the use of new on-shell methods, 4-dimensional unitarity cuts combined with on-shell recursions relations, by computing the A_4^{(1)}(phi,1^-,2^-,3^+,4^+) amplitude in the large top mass limit where the Higgs boson couples to gluons through an effective interaction.
Super $q$-Howe duality and web categories

We use super $q$-Howe duality to provide diagrammatic presentations of an idempotented form of the Hecke algebra and of categories of $\mathfrak{gl}_N$-modules (and, more generally, $\mathfrak{gl}_{N|M}$-modules) whose objects are tensor generated by exterior and symmetric powers of the vector representations. As an application, we give a representation theoretic explanation and a diagrammatic version of a known symmetry of colored HOMFLY--PT polynomials.
Parton showers with quantum interference

We specify recursive equations that could be used to generate a lowest order parton shower for hard scattering in hadron-hadron collisions. The formalism is based on the factorization soft and collinear interactions from relatively harder interactions in QCD amplitudes. It incorporates quantum interference between different amplitudes in those cases in which the interference diagrams have leading soft or collinear singularities. It incorporates the color and spin information carried by partons emerging from a hard interaction. One motivation for this work is to have a method that can naturally cooperate with next-to-leading order calculations.
Unified field theory on the basis of the projective theory of relativity

A unified field theory is developed on the basis of the five-dimensional vacuum equations R/sub munu/ = 0 in the projective theory of relativity. The four-dimensional field equations following from R/sub munu/ = 0 by projection are a generalized Einstein-Maxwell theory, for which the generalization is given by a scalar field. The particle concept based on these equations represents the intrinsic particle properties, which are the rest mass, or the energy in case of photons and neutrinos, the charge and the spin by integrals of the field distribution extended over spacelike hypersurfaces. The energy concept is based on Moller's energy-momentum complex. Moller's argument against his energy-momentum complex is discussed and refuted. The spin concept is derived from the axial symmetry of the field distribution. The stationary axially symmetric field is studied in detail. In the spherically symmetric static case the solutions of the field equations are given and investigated for their particle properties. It is shown that one and only one type of solution yields a good approach to the distribution of charge and rest mass in the proton. However, none of the spherically symmetric solutions represents the electron.
Matroids of Gain Graphs in Applied Discrete Geometry

A G-gain graph is a graph whose oriented edges are labeled invertibly from a group G. Zaslavsky proposed two matroids of G-gain graphs, called frame matroids and lift matroids, and investigated linear representations of them. Each matroid has a canonical representation over a field F if G is isomorphic to a subgroup of F^{\times} in the case of frame matroids or G is isomorphic to an additive subgroup of F in the case of lift matroids. The canonical representation of the frame matroid of a complete graph is also known as a Dowling geometry, as it was first introduced by Dowling for finite groups. In this paper, we extend these matroids in two ways. The first one is extending the rank function of each matroid, based on submodular functions over G. The resulting rank function generalizes that of the union of frame matroids or lift matroids. Another one is extending the canonical linear representation of the union of d copies of a frame matroid or a lift matroid, based on linear representations of G on a d-dimensional vector space. We show that linear matroids of the latter extension are indeed special cases of the first extensions, as in the relation between Dowling geometries and frame matroids. We also discuss an attempt to unify the extension of frame matroids and that of lift matroids. This work is motivated from recent research on the combinatorial rigidity of symmetric graphs. As special cases, we give several new results on this topic, including combinatorial characterizations of the symmetry-forced rigidity of generic body-bar frameworks with point group symmetries or crystallographic symmetries and the symmetric parallel redrawability of generic bar-joint frameworks with point group symmetries or crystallographic symmetries.
Triplet energy transfer in conjugated polymers. I. Experimental investigation of a weakly disordered compound

Efficient triplet exciton emission has allowed improved operation of organic light-emitting diodes LEDs. To enhance the device performance, it is necessary to understand what governs the motion of triplet excitons through the organic semiconductor. Here, we have investigated triplet diffusion using a model compound that has weak energetic disorder. The Dexter-type triplet energy transfer is found to be thermally activated down to a transition temperature TT, below which the transfer rate is only weakly temperature dependent. We show that above the transition temperature, Dexter energy transfer can be described within the framework of Marcus theory. We suggest that below TT, the nature of the transfer changes from phonon-assisted hopping to quantummechanical tunneling. The lower electron-phonon coupling and higher electronic coupling in the polymer compared to the monomer results in an enhanced triplet diffusion rate.
Multi-convex Inequality-constrained Alternating Direction Method of Multipliers

In recent years, although the Alternating Direction Method of Multipliers (ADMM) has been empirically applied widely for many multi-convex applications, delivering an impressive performance in areas such as adversarial learning and nonnegative matrix factorization, there remains a dearth of generic work on multi-convex ADMM with a theoretical guarantee under mild conditions. In this paper, we propose a novel generic framework of multi-convex inequality-constrained ADMM (miADMM) with multiple coupled variables in both objective and constraints. Theoretical properties such as convergence conditions and properties are discussed and proven. Several important applications are discussed as special cases under our miADMM framework. These cases are from a wide variety of topical machine learning problems. Extensive experiments on one synthetic dataset and ten real-world datasets related to multiple applications demonstrate the proposed framework's effectiveness, scalability, and convergence properties.
Unfrustration Condition and Degeneracy of Qudits on Trees

We generalize the previous results of [1] by proving unfrustration condition and degeneracy of the ground states of qudits (d-dimensional spins) on a k-child tree with generic local interactions. We find that the dimension of the ground space grows doubly exponentially in the region where rk 1. Further, we extend the results in [1] by proving that there are no zero energy ground states when r>(d^2)/4 for k=1 implying that the effective Hamiltonian is invertible.
Corrective control: stability analysis of Unified Controller combining frequency control and congestion management

This paper analyses stability of the Unified Controller (UC) that combines frequency control and congestion management and therefore makes it possible to move from preventive to corrective power system control. Earlier work by the authors of UC proved asymptotic stability of the methodology but the proof was based on a simplified first-order model of the turbine and turbine governor. We show that a higher order model of the turbine governor leads to eigenvalues with small but positive real parts. Consequently, we develop a modification of the methodology that decouples the physical and control systems and therefore results in all the eigenvalues having negative real parts. We illustrate the effectiveness of the modification on a realistic model of 39-bus model of New England power system implemented in Power System Toolbox (PST).
Subshifts with sparse traces

We study two-dimensional subshifts whose horizontal trace (a.k.a. projective subdynamics) contains only points of finite support. Our main result is a classification result for such subshifts satisfying a minimality property. As corollaries, we obtain new proofs for various known results on traces of SFTs, nilpotency and decidability of cellular automata, topological full groups and the subshift of prime numbers. We also construct various (sofic) examples illustrating the concepts.
Very-high-efficiency double-heterostructure copper phthalocyanine/C60 photovoltaic cells

We demonstrate an external power conversion efficiency of (3.6±0.2)% under AM1.5 spectral illumination of 150 mW/cm2 (1.5 suns) with vacuum-deposited copper phthalocyanine/C60 thin-film double-heterostructure photovoltaic cells incorporating an exciton-blocking layer (EBL). We show that the anode work function influences the photocarrier collection characteristics through the built-in electric field. The cell parameters are less sensitive to the cathode work function, which is attributed to cathode-induced defect states in the EBL energy gap. The presence of these defect states also explains the surprisingly low resistance of the EBL to electron transport. We anticipate significant further improvements in power conversion efficiency by employing optimal structures in light-trapping geometries.
Investigating Generate and Test for Online Representation Search with Softmax Outputs

Modern representation learning methods perform well on offline tasks and primarily revolve around batch updates. However, batch updates preclude those methods from focusing on new experience, which is essential for fast online adaptation. In this thesis, we study an online and incremental representation search algorithm called Generate and Test, which continually replaces the least useful features with newly generated features. In this algorithm, the utility of features is estimated by a heuristic tester based on the magnitude of their corresponding outgoing weights; the least useful features are those with the smallest weight magnitudes. Generate and Test was developed and evaluated only on single-output regression problems. However, it has not been investigated in multi-output regression problems. Moreover, it is not clear that magnitude-based testers are appropriate for other outputs such as softmax. In this thesis, we investigate Generate and Test in these new cases and introduce testbeds for online representation learning in multi-output regression, classification, and reinforcement learning environments with discrete action spaces. We show that magnitude-based feature utility may give wrong estimates of the utility when softmax outputs are used, for example, in classification and discrete control tasks. We propose a new tester to extend the scope of the Generate and Test algorithm to these cases. We empirically show that this new tester can improve representations better than the magnitude-based tester. Thus, ours is the first work to make the Generate and Test algorithm applicable beyond supervised regression tasks. ii