Could saturation effects be visible in a future electron-ion collider?

We expect to observe parton saturation in a future electron-ion collider. In this Letter we discuss this expectation in more detail considering two different models which are in good agreement with the existing experimental data on nuclear structure functions. In particular, we study the predictions of saturation effects in electron-ion collisions at high energies, using a generalization for nuclear targets of the b-CGC model, which describes the ep HERA quite well. We estimate the total. longitudinal and charm structure functions in the dipole picture and compare them with the predictions obtained using collinear factorization and modern sets of nuclear parton distributions. Our results show that inclusive observables are not very useful in the search for saturation effects. In the small x region they are very difficult to disentangle from the predictions of the collinear approaches. This happens mainly because of the large uncertainties in the determination of the nuclear parton distribution functions. On the other hand, our results indicate that the contribution of diffractive processes to the total cross section is about 20% at large A and small Q(2), allowing for a detailed study of diffractive observables. The study of diffractive processes becomes essential to observe parton Saturation. (C) 2008 Elsevier B.V. All rights reserved.

Higgs-boson production at small transverse momentum

Using methods from effective field theory, we have recently developed a novel, systematic framework for the calculation of the cross sections for electroweak gauge-boson production at small and very small transverse momentum q T , in which large logarithms of the scale ratio m V /q T are resummed to all orders. This formalism is applied to the production of Higgs bosons in gluon fusion at the LHC. The production cross section receives logarithmically enhanced corrections from two sources: the running of the hard matching coefficient and the collinear factorization anomaly. The anomaly leads to the dynamical generation of a non-perturbative scale q∗~mHe−const/αs(mH)≈8 GeV, which protects the process from receiving large long-distance hadronic contributions. We present numerical predictions for the transverse-momentum spectrum of Higgs bosons produced at the LHC, finding that it is quite insensitive to hadronic effects.

Factorization and non-local 1/m b corrections in the decay B X s gamma

In this thesis, a systematic analysis of the bar B to X_sgamma photon spectrum in the endpoint region is presented. The endpoint region refers to a kinematic configuration of the final state, in which the photon has a large energy m_b-2E_gamma = O(Lambda_QCD), while the jet has a large energy but small invariant mass. Using methods of soft-collinear effective theory and heavy-quark effective theory, it is shown that the spectrum can be factorized into hard, jet, and soft functions, each encoding the dynamics at a certain scale. The relevant scales in the endpoint region are the heavy-quark mass m_b, the hadronic energy scale Lambda_QCD and an intermediate scale sqrt{Lambda_QCD m_b} associated with the invariant mass of the jet. It is found that the factorization formula contains two different types of contributions, distinguishable by the space-time structure of the underlying diagrams. On the one hand, there are the direct photon contributions which correspond to diagrams with the photon emitted directly from the weak vertex. The resolved photon contributions on the other hand arise at O(1/m_b) whenever the photon couples to light partons. In this work, these contributions will be explicitly defined in terms of convolutions of jet functions with subleading shape functions. While the direct photon contributions can be expressed in terms of a local operator product expansion, when the photon spectrum is integrated over a range larger than the endpoint region, the resolved photon contributions always remain non-local. Thus, they are responsible for a non-perturbative uncertainty on the partonic predictions. In this thesis, the effect of these uncertainties is estimated in two different phenomenological contexts. First, the hadronic uncertainties in the bar B to X_sgamma branching fraction, defined with a cut E_gamma > 1.6 GeV are discussed. It is found, that the resolved photon contributions give rise to an irreducible theory uncertainty of approximately 5 %. As a second application of the formalism, the influence of the long-distance effects on the direct CP asymmetry will be considered. It will be shown that these effects are dominant in the Standard Model and that a range of -0.6 < A_CP^SM < 2.8 % is possible for the asymmetry, if resolved photon contributions are taken into account.

Factorization and N3LLp+NNLO predictions for the Higgs cross section with a jet veto

We have recently derived a factorization formula for the Higgs-boson production cross section in the presence of a jet veto, which allows for a systematic resummation of large Sudakov logarithms of the form αn s lnm(pveto T /mH), along with the large virtual corrections known to affect also the total cross section. Here we determine the ingredients entering this formula at two-loop accuracy. Specifically, we compute the dependence on the jet-radius parameter R, which is encoded in the two-loop coefficient of the collinear anomaly, by means of a direct, fully analytic calculation in the framework of soft-collinear effective theory. We confirm the result obtained by Banfi et al. from a related calculation in QCD, and demonstrate that factorization-breaking, soft-collinear mixing effects do not arise at leading power in pveto T /mH, even for R = O(1). In addition, we extract the two-loop collinear beam functions numerically. We present detailed numerical predictions for the jet-veto cross section with partial next-to-next-to-next-to-leading logarithmic accuracy, matched to the next-to-next-to-leading order cross section in fixed-order perturbation theory. The only missing ingredients at this level of accuracy are the three-loop anomaly coefficient and the four-loop cusp anomalous dimension, whose numerical effects we estimate to be small.

Factorization and resummation for transverse thrust

We analyze transverse thrust in the framework of Soft Collinear Effective Theory and obtain a factorized expression for the cross section that permits resummation of terms enhanced in the dijet limit to arbitrary accuracy. The factorization theorem for this hadron-collider event-shape variable involves collinear emissions at different virtualities and suffers from a collinear anomaly. We compute all its ingredients at the one-loop order, and show that the two-loop input for next-to-next-to-leading logarithmic accuracy can be extracted numerically, from existing fixed-order codes.

Injury narrative text classification using factorization model

Narrative text is a useful way of identifying injury circumstances from the routine emergency department data collections. Automatically classifying narratives based on machine learning techniques is a promising technique, which can consequently reduce the tedious manual classification process. Existing works focus on using Naive Bayes which does not always offer the best performance. This paper proposes the Matrix Factorization approaches along with a learning enhancement process for this task. The results are compared with the performance of various other classification approaches. The impact on the classification results from the parameters setting during the classification of a medical text dataset is discussed. With the selection of right dimension k, Non Negative Matrix Factorization-model method achieves 10 CV accuracy of 0.93.

Bauer Method of MVDR Spectral Factorization for Pitch Modification in the Source Domain

In our earlier work [1], we employed MVDR (minimum variance distortionless response) based spectral estimation instead of modified-linear prediction method [2] in pitch modification. Here, we use the Bauer method of MVDR spectral factorization, leading to a causal inverse filter rather than a noncausal filter setup with MVDR spectral estimation [1]. Further, this is employed to obtain source (or residual) signal from pitch synchronous speech frames. The residual signal is resampled using DCT/IDCT depending on the target pitch scale factor. Finally, forward filters realized from the above factorization are used to get pitch modified speech. The modified speech is evaluated subjectively by 10 listeners and mean opinion scores (MOS) are tabulated. Further, modified bark spectral distortion measure is also computed for objective evaluation of performance. We find that the proposed algorithm performs better compared to time domain pitch synchronous overlap [3] and modified-LP method [2]. A good MOS score is achieved with the proposed algorithm compared to [1] with a causal inverse and forward filter setup.

A model based factorization approach for dense 3D recovery from monocular video

Feature track matrix factorization based methods have been attractive solutions to the Structure-front-motion (Sfnl) problem. Group motion of the feature points is analyzed to get the 3D information. It is well known that the factorization formulations give rise to rank deficient system of equations. Even when enough constraints exist, the extracted models are sparse due the unavailability of pixel level tracks. Pixel level tracking of 3D surfaces is a difficult problem, particularly when the surface has very little texture as in a human face. Only sparsely located feature points can be tracked and tracking error arc inevitable along rotating lose texture surfaces. However, the 3D models of an object class lie in a subspace of the set of all possible 3D models. We propose a novel solution to the Structure-from-motion problem which utilizes the high-resolution 3D obtained from range scanner to compute a basis for this desired subspace. Adding subspace constraints during factorization also facilitates removal of tracking noise which causes distortions outside the subspace. We demonstrate the effectiveness of our formulation by extracting dense 3D structure of a human face and comparing it with a well known Structure-front-motion algorithm due to Brand.

Design space exploration of systolic realization of QR factorization on a runtime reconfigurable platform

In the world of high performance computing huge efforts have been put to accelerate Numerical Linear Algebra (NLA) kernels like QR Decomposition (QRD) with the added advantage of reconfigurability and scalability. While popular custom hardware solution in form of systolic arrays can deliver high performance, they are not scalable, and hence not commercially viable. In this paper, we show how systolic solutions of QRD can be realized efficiently on REDEFINE, a scalable runtime reconfigurable hardware platform. We propose various enhancements to REDEFINE to meet the custom need of accelerating NLA kernels. We further do the design space exploration of the proposed solution for any arbitrary application of size n × n. We determine the right size of the sub-array in accordance with the optimal pipeline depth of the core execution units and the number of such units to be used per sub-array.

Study of Low Temperature Magnetic Properties of a Single Chain Magnet with Alternate Isotropic and Non-collinear Anisotropic Units

Here we study thermodynamic properties of an important class of single-chain magnets (SCMs), where alternate units are isotropic and anisotropic with anisotropy axes being non-collinear. This class of SCMs shows slow relaxation at low temperatures which results from the interplay of two different relaxation mechanisms, namely dynamical and thermal. Here anisotropy is assumed to be large and negative, as a result, anisotropic units behave like canted spins at low temperatures; but even then simple Ising-type model does not capture the essential physics of the system due to quantum mechanical nature of the isotropic units. We here show how statistical behavior of this class of SCMs can be studied using a transfer matrix (TM) method. We also, for the first time, discuss in detail how weak inter-chain interactions can be treated by a TM method. The finite size effect is also discussed which becomes important for low temperature dynamics. At the end of this paper, we apply this technique to study a real helical chain magnet.

Hybrid online non-negative matrix factorization for clustering of documents

When document corpus is very large, we often need to reduce the number of features. But it is not possible to apply conventional Non-negative Matrix Factorization(NMF) on billion by million matrix as the matrix may not fit in memory. Here we present novel Online NMF algorithm. Using Online NMF, we reduced original high-dimensional space to low-dimensional space. Then we cluster all the documents in reduced dimension using k-means algorithm. We experimentally show that by processing small subsets of documents we will be able to achieve good performance. The method proposed outperforms existing algorithms.

Multivariate Granger causality: an estimation framework based on factorization of the spectral density matrix

Granger causality is increasingly being applied to multi-electrode neurophysiological and functional imaging data to characterize directional interactions between neurons and brain regions. For a multivariate dataset, one might be interested in different subsets of the recorded neurons or brain regions. According to the current estimation framework, for each subset, one conducts a separate autoregressive model fitting process, introducing the potential for unwanted variability and uncertainty. In this paper, we propose a multivariate framework for estimating Granger causality. It is based on spectral density matrix factorization and offers the advantage that the estimation of such a matrix needs to be done only once for the entire multivariate dataset. For any subset of recorded data, Granger causality can be calculated through factorizing the appropriate submatrix of the overall spectral density matrix.

Anisotropic magnetic couplings and structure-driven canted to collinear transitions in Sr2IrO4 by magnetically constrained noncollinear DFT

We study the canted magnetic state in Sr2IrO4 using fully relativistic density functional theory (DFT) including an on-site Hubbard U correction. A complete magnetic phase diagram with respect to the tetragonal distortion and the rotation of IrO6 octahedra is constructed, revealing the presence of two types of canted to collinear magnetic transitions: a spin-flop transition with increasing tetragonal distortion and a complete quenching of the basal weak ferromagnetic moment below a critical octahedral rotation. Moreover, we put forward a scheme to study the anisotropic magnetic couplings by mapping magnetically constrained noncollinear DFT onto a general spin Hamiltonian. This procedure allows for the simultaneous account and direct control of the lattice, spin, and orbital interactions within a fully ab initio scheme. We compute the isotropic, single site anisotropy and Dzyaloshinskii-Moriya (DM) coupling parameters, and clarify that the origin of the canted magnetic state in Sr2IrO4 arises from the structural distortions and the competition between isotropic exchange and DM interactions.

Average Overlap for Clustering Incomplete Data using Symmetric Non-Negative Matrix Factorization

Clustering techniques which can handle incomplete data have become increasingly important due to varied applications in marketing research, medical diagnosis and survey data analysis. Existing techniques cope up with missing values either by using data modification/imputation or by partial distance computation, often unreliable depending on the number of features available. In this paper, we propose a novel approach for clustering data with missing values, which performs the task by Symmetric Non-Negative Matrix Factorization (SNMF) of a complete pair-wise similarity matrix, computed from the given incomplete data. To accomplish this, we define a novel similarity measure based on Average Overlap similarity metric which can effectively handle missing values without modification of data. Further, the similarity measure is more reliable than partial distances and inherently possesses the properties required to perform SNMF. The experimental evaluation on real world datasets demonstrates that the proposed approach is efficient, scalable and shows significantly better performance compared to the existing techniques.

Towards an exact factorization of the molecular wave function

An exact single-product factorisation of the molecular wave function for the timedependent Schrodinger equation is investigated by using an ansatz involving a phasefactor. By using the Frenkel variational method, we obtain the Schrodinger equations for the electronic and nuclear wave functions. The concept of a potential energy surface (PES) is retained by introducing a modified Hamiltonian as suggested earlier by Cederbaum. The parameter in the phase factor is chosen such that the equations of motion retain the physically appealing Born- Oppenheimer-like form, and is therefore unique.