Way Of Regularization Research Articles

A network-based matrix factorization framework for ceRNA co-modules recognition of cancer genomic data.

With the development of high-throughput technologies, the accumulation of large amounts of multidimensional genomic data provides an excellent opportunity to study the multilevel biological regulatory relationships in cancer. Based on the hypothesis of competitive endogenous ribonucleic acid (RNA) (ceRNA) network, lncRNAs can eliminate the inhibition of microRNAs (miRNAs) on their target genes by binding to intracellular miRNA sites so as to improve the expression level of these target genes. However, previous studies on cancer expression mechanism are mostly based on individual or two-dimensional data, and lack of integration and analysis of various RNA-seq data, making it difficult to verify the complex biological relationships involved. To explore RNA expression patterns and potential molecular mechanisms of cancer, a network-regularized sparse orthogonal-regularized joint non-negative matrix factorization (NSOJNMF) algorithm is proposed, which combines the interaction relations among RNA-seq data in the way of network regularization and effectively prevents multicollinearity through sparse constraints and orthogonal regularization constraints to generate good modular sparse solutions. NSOJNMF algorithm is performed on the datasets of liver cancer and colon cancer, then ceRNA co-modules of them are recognized. The enrichment analysis of these modules shows that >90% of them are closely related to the occurrence and development of cancer. In addition, the ceRNA networks constructed by the ceRNA co-modules not only accurately mine the known correlations of the three RNA molecules but also further discover their potential biological associations, which may contribute to the exploration of the competitive relationships among multiple RNAs and the molecular mechanisms affecting tumor development.

Blunt body impact onto viscoelastic floating ice plate with a soft layer on its upper surface

Two-dimensional vertical impact of a rigid blunt body onto a floating ice plate is studied. The problem is coupled and unsteady. The liquid is inviscid, incompressible, and of infinite depth. The ice floe is modeled as a thin viscoelastic plate of constant thickness. The plate edges are free of bending stresses and shear forces. The upper surface of the plate is covered with a viscoelastic layer of constant small thickness and negligible inertia. The reaction force of this soft layer is predicted by a nonlinear and one-dimensional Winkler-Kelvin-Voigt model, which does not permit a contact between the rigid body and the ice plate. The soft layer may describe either the presence of snow on the ice or a layer of crushed ice in the place of impact, or can be considered as a way of regularization of problems with concentrated loads. The rigid body touches the upper surface of the soft layer and then suddenly starts to move downward with constant velocity. It is shown that the strains in the ice plate caused by the impact are weakly dependent on the characteristics of the soft layer. The magnitudes and distributions of the strains are studied depending on the length of the ice plate, retardation time of the ice model, thickness of the plate, shape of the rigid body, place of impact, and the impact speed. The value of the retardation time in the soft layer model is discussed with relation to the ice crushing by impact.

Contact Interactions in One-Dimensional Quantum Mechanics: a Family of Generalized б'-Potentials

A “one-point” approximation is proposed to investigate the transmission of electrons through the extra thin heterostructures composed of two parallel plane layers. The typical example is the bilayer for which the squeezed potential profile is the derivative of Dirac’s delta function. The Schr¨odinger equation with this singular one-dimensional profile produces a family of contact (point) interactions each of which (called a “distributional” б′-potential) depends on the way of regularization. The discrepancies widely discussed so far in the literature regarding the family of delta derivative potentials are eliminated using a two-scale power-connecting parametrization of the bilayer potential that enables one to extend the family of distributional б′-potentials to a whole class of “generalized” б′-potentials. In a squeezed limit of the bilayer structure to zero thickness, the resonant tunneling through this structure is shown to occur in the form of sharp peaks located on the sets of Lebesgue’s measure zero (called resonance sets). A four-dimensional parameter space is introduced for the representation of these sets. The transmission on the complement sets in the parameter space is shown to be completely opaque.

1D Schrödinger operators with Coulomb-like potentials

We study the convergence of 1D Schrödinger operators Hε with the potentials which are regularizations of a class of pseudopotentials having, in particular, the form αδ′(x) + βδ(x) + γ/|x| or αδ′(x) + βδ(x) + γ/x. The limit behavior of Hε in the norm resolvent topology, as ε → 0, essentially depends on a way of regularization of the Coulomb potential and the existence of zero-energy resonances for δ′-like potential. All possible limits are described in terms of point interactions at the origin. As a consequence of the convergence results, different kinds of L∞(R)-approximations to the even and odd Coulomb potentials, both penetrable and impenetrable in the limit, are constructed.

Migrating Knowledge between Physical Scenarios Based on Artificial Neural Networks

Deep learning is known to be data-hungry, which hinders its application in many areas of science when data sets are small. Here, we propose to use transfer learning methods to migrate knowledge between different physical scenarios and significantly improve the prediction accuracy of artificial neural networks trained on a small data set. This method can help reduce the demand for expensive data by making use of additional inexpensive data. First, we demonstrate that, in predicting the transmission from multilayer photonic film, the relative error rate is reduced by 50.5% (23.7%) when the source data comes from 10-layer (8-layer) films and the target data comes from 8-layer (10-layer) films. Second, we show that the relative error rate is decreased by 19.7% when knowledge is transferred between two very different physical scenarios: transmission from multilayer films and scattering from multilayer nanoparticles. Next, we propose a multitask learning method to improve the performance of different physical scenarios simultaneously in which each task only has a small data set. Finally, we demonstrate that the transfer learning framework truly discovers the common underlying physical rules instead of just performing a certain way of regularization.

Flexible sparse regularization

The seminal paper of Daubechies, Defrise, DeMol made clear that spaces with and p-powers of the corresponding norms are appropriate settings for dealing with reconstruction of sparse solutions of ill-posed problems by regularization. It seems that the case p = 1 provides the best results in most of the situations compared to the cases . An extensive literature gives great credit also to using spaces with together with the corresponding quasi-norms, although one has to tackle challenging numerical problems raised by the non-convexity of the quasi-norms. In any of these settings, either superlinear, linear or sublinear, the question of how to choose the exponent p has been not only a numerical issue, but also a philosophical one. In this work we introduce a more flexible way of sparse regularization by varying exponents. We introduce the corresponding functional analytic framework, that leaves the setting of normed spaces but works with so-called F-norms. One curious result is that there are F-norms which generate the ℓ1 space, but they are strictly convex, while the ℓ1-norm is just convex.

Excluding chaos by regularizing a macro model with Hicksian nonlinearity

A piecewise linear macro model with ceilings and floors is perturbed in the way of regularization to interpret economic reality more reasonably. Hopf bifurcations for these perturbed models are obtained, excluding chaos which, as is well known, takes place in the unperturbed version. The study reveals the non-chaotic nature of the model.

Las composiciones de extranjeros en la Nueva España, 1595–1700

In the early 1590s, Philip II of Spain recognized that the royal treasury was exhausted. In an effort to recoup monetary resources, he imposed several taxes in the American viceroyalties. One of them was the composición (settlement) for foreigners. The composición has been interpreted as a way of legalization and regularization of illegal foreigners. We argue instead that composición was a penalty, executed by the king in order to distribute Royal Patronage. We analyze its origins and transformations, as well as the problems experienced by the king’s servants, and the solutions they found for its application in Mexico between 1595 and 1694. Finally, we examine how the composición was received and the impact it had on foreigners.

Non-conformal limit of AGT relation from the 1-point torus conformal block

Given a 4d N=2 SUSY gauge theory, one can construct the Seiberg-Witten prepotentional, which involves a sum over instantons. Integrals over instanton moduli spaces require regularisation. For UV-finite theories the AGT conjecture favours particular, Nekrasov's way of regularization. It implies that Nekrasov's partition function equals conformal blocks in 2d theories with W_{N_c} chiral algebra. For $N_c=2$ and one adjoint multiplet it coincides with a torus 1-point Virasoro conformal block. We check the AGT relation between conformal dimension and adjoint multiplet's mass in this case and investigate the limit of the conformal block, which corresponds to the large mass limit of the 4d theory e.i. the asymptotically free 4d N=2 supersymmetric Yang-Mills theory. Though technically more involved, the limit is the same as in the case of fundamental multiplets, and this provides one more non-trivial check of AGT conjecture.

Dimensional taming of mass singularities in QCD corrections to weak radiative decays of quarks

Lowest order QCD corrections to the rate of the b→sγ decay induced by effective weak-interaction dipole operators are calculated by using dimensional regularization. The existing calculations of the rate all appear to have had recourse to dimensional reduction as a way of regularization. It is shown that the rate does not depend on which one of the two methods of regularization is used as long as the s quark is considered massive, because both regularizations give rise to the same on-shell wave function renormalization and because of the validity of the Bloch–Nordsieck theorem. In the heavy b-quark limit, realized by treating the s quark as massless, however, the two regularization methods give different results. It is argued that only dimensional regularization leads to correct results unless some unconventional on-shell wave function renormalization of massless fermion fields is adopted.

Regularization and existence of solutions in the equilibrium problem for an elastoplastic plate

UDC 517.9 At present, there are many articles devoted to the solvability of the boundary value problems describing deformation of static and quasistatic ideally elastoplastic bodies. Namely, solvability of variational inequalities resulting from the original (exact) statements of boundary value problems is proven in the case of quasistatic deformation for the flow-type models and in the case of static deformation for the Hencky-type models [1-7]. A peculiarity of solutions to the variational inequalities is the fact that some boundary conditions are lost. The smoothness assumption on a solution to the variational inequality does not allow us to establish the presence of the lost boundary conditions, since the set of feasible stresses is not a vector space. It was demonstrated in [8-11] that in the case of one-dimensional models of elastoplastic deformation (beam, rod, etc.) a solution to the variational inequality does not loose the boundary conditions that are involved in the original statement of the boundary value problem; i.e., all boundary conditions hold. Until recently, there were no such results for three-dimensional (two-dimensional) models of elastoplasticity. In the present article, we prove an existence theorem for the equilibrium problem for an elastoplastic plate which guarantees validity of all boundary conditions. Moreover, we consider domains with smooth boundaries as well as domains with cuts. The proof is based on a special combination of the regularization method and the penalty method. Namely, we apply elliptic regularization for solving the penalized boundary value problem that approximates the original elastoplastic problem. We obtain an existence theorem for the original problem by passing to the limit over the regularization and penalty parameters. The proposed way of regularization turns out to be rather effective and useful for analysis of other elastoplastic problems. The essence of the method consists in the fact that the regularization of the penalized equations is accompanied by special regularization of the boundary conditions. 1. A domain with smooth boundary. Suppose that fl C R 2 is a bounded domain with smooth boundary F and �9 : R 3 ---* R is a continuous convex function. The equilibrium problem for an elastoplastic plate is stated as follows [12]: Find functions w, m = {mij}, and ~ii, i,j = 1, 2, in satisfying the following equations and inequalities: -rnii,ij = f,