The conjugate gradient algorithm on a general class of spiked covariance matrices

We consider the conjugate gradient algorithm applied to a general class of spiked sample covariance matrices. The main result of the paper is that the norms of the error and residual vectors at any finite step concentrate on deterministic values determined by orthogonal polynomials with respect to a deformed Marchenko–Pastur law. The first-order limits and fluctuations are shown to be universal. Additionally, for the case where the bulk eigenvalues lie in a single interval we show a stronger universality result in that the asymptotic rate of convergence of the conjugate gradient algorithm only depends on the support of the bulk, provided the spikes are well-separated from the bulk. In particular, this shows that the classical condition number bound for the conjugate gradient algorithm is pessimistic for spiked matrices.

Aspiration dynamics generate robust predictions in heterogeneous populations

Update rules, which describe how individuals adjust their behavior over time, affect the outcome of social interactions. Theoretical studies have shown that evolutionary outcomes are sensitive to model details when update rules are imitation-based but are robust when update rules are self-evaluation based. However, studies of self-evaluation based rules have focused on homogeneous population structures where each individual has the same number of neighbors. Here, we consider heterogeneous population structures represented by weighted networks. Under weak selection, we analytically derive the condition for strategy success, which coincides with the classical condition of risk-dominance. This condition holds for all weighted networks and distributions of aspiration levels, and for individualized ways of self-evaluation. Our findings recover previous results as special cases and demonstrate the universality of the robustness property under self-evaluation based rules. Our work thus sheds light on the intrinsic difference between evolutionary dynamics under self-evaluation based and imitation-based update rules.

Migrants’ Access to Social Protection in France

After a long judicial fight between the 1970s and the late 1990s leading to the abolition of the condition of nationality that excluded foreigners from non-contributory benefits, and in a context of publicly debated restrictive immigration policies, other restrictive conditions were either reinforced or introduced in order to curb access to social protection for foreigners in France. A new condition of regularity for the access of foreigners to most social protection schemes was introduced and/or extended, especially since 1993. In a growing xenophobic context, restrictions were presented as a means to deter immigration and save the Welfare State placed under strong budgetary constraints. The classical condition of residence was also reactivated in a way to place more restrictions. New requirements, such as a condition of anteriority of presence and a condition of anteriority (seniority) of regular residence, were developed to exclude more non-EU migrants, despite their regular situation.

Bio-polysaccharide electrolyte gated photoelectric synergic coupled oxide neuromorphic transistor with Pavlovian activities

A photoelectric synergic coupled oxide neuromorphic transistor was fabricated, demonstrating photoelectric synergic spatiotemporal integration activities and Pavlovian classical condition activities.

Optimization of the break-even point for non-homogeneous products sales

Break-even point analysis is a classic management accounting tool. In the case of the sale of one product, the notion of the break-even point is well described in the literature, conceptually simple, and relatively easy to apply in business practice. However, when it comes to heterogeneous sales, consisting of various products, this problem is presented less frequently, and the methods used in this case exploit rather arbitrary and often ambiguous criteria. The aim of the article is to present and analyze alternative ways of determining break-even points for non-homogeneous sales based on econometric modeling methods. Production levels determined by the proposed methods meet the classical condition set for the break-even point, and in addition are optimal from the point of view of criteria used in the economic analysis. Three methods were presented: first – based on the classic criterion of profit maximization and linear programming, second – minimizing variable production costs and taking into account the scale effects on the production costs, and third – taking into account the random aspect of the business operations and maximizing the probability of profitability. According to the authors' knowledge, the proposed methods are original and are not known in the existing literature on the subject.

Comment on ‘The cutting of metals by plastic buckling’ by Udupa et al .

In a recent paper on machining annealed copper at a low cutting speed, and at an uncut chip thickness one-tenth of the mean grain size of the copper, Udupa et al . ( Proc. R. Soc A 473 , 20160863, doi:10.1098/rspa.2016.0863 ) report chip thicknesses larger than 10 times the uncut thickness and then a new mode of chip formation. Plastic bulging occurs in the surface of the copper ahead of the tool, leading to chip formation by a series of folds. The strain in the chip is less than that expected in a chip formed by shear according to long-standing classical theory. The authors suggest that the foundations of that theory need to be re-examined. In response, continuum mechanics numerical simulations presented here show a continuous transition from the classical condition towards that observed by Udupa et al . as the ratio of chip thickness to uncut thickness increases above approximately 7. Bulging is obtained by introducing (approximately) material heterogeneity to the simulations at a grain size scale but whether such heterogeneity is essential for the bulging flows remains an open question.

THE SCRIPTURE IN THE PUBLISHING PLANS OF THE MOTHER SEE HOLY ETCHMIADZIN

The Armenian Church from the beginning had a great interest in publishing the Holy Bible. However the political conditions until 70-ties of XVIII century didnt allow to develop the publishing business neither in Western, nor in Eastern Armenia. Exactly because of this reason the Armenian catholicoses tried at any cost to support the publishing business abroad. In this period the activity of printer's ''Holy Etchmiadzin and st.Sargis'', which was established in Amsterdam, became a new phenomenon in the Armenian book-printing. By virtue of work of this printinghouse and the efforts of former chancellor of the Mother See Voskan Yerevantsi the first Armenian Bible came into being. In the XVIII-XIX centuries the political conditions didnt allow the Mother See to focus on the research and preparation of the text of the Bible.It seems that Mother See Holy Etchmiadzin yielded to Mekhitarists the primacy of research in this field. The catholicoses Macar Teghutetsi and Khrimean Hairik, lived in the late 19th - early 20th century, focused attention of the congregation of Vagharshapat on the republication of the biblical texts. Unfortunately the work was interrupted. As it was unclear how to present the text of the Bible to the reader. If Karapet Ter-Mkrtchean set a goal to restore the classical condition of the text, the greater part of the spiritual estate required in a short time to publish a Bible that satisfies the religious needs of the Church. Another part of the believers and Church ministers hoped to have a Bible translated into a language understandable to the people. I suppose that these opposite goals also contributed to the termination of the work. One should regret that to this day it is not known where are kept the results of the work done under the leadership of K. Ter-Mkrtchean. From the standpoint of stimulating the publication of the Bible important was the celebration of the 300th anniversary of publication of the Bible of Voskan, which was initiated by catholicos Vazgen I. The rather serried phalanx of armenologists got down to work, and thanks to their efforts in 1996 the Bible was translated into the Eastern Armenian language. The most important achievment of the last decades was the publication of dozens of scientific biblical texts. Today the preparation of the scientific text of the Bible remains one of the most important tasks facing modern Armenology and the Mother See Holy Etchmiadzin.

Vibrational Analysis of Damped Orthotropic Rectangular Plates with Simple Support on Elastic Winkler Foundation Subjected to Moving Loads

The model of a damped orthotropic rectangular plate resting on a Winkler foundation with a simple support has the fourth order differential equation governing it, which is reduced to a second order coupled differential equation by separating the variables. The coupled differential equation was solved using numerical schemes .The classical condition used as an illustrative example is the simple support condition. It is observed that damping plays a very significant role in the vibration of solid structures, as it has been shown that the deflection profile depends greatly on the damping ratio. The deflection profile also proves to be more stable in the presence of foundation coupled with viscous damping. The results obtained were discussed and graphically presented.

A NECESSARY AND SUFFICIENT CONDITION FOR THE NON-EMPTINESS OF THE SOCIALLY STABLE CORE IN STRUCTURED TU-GAMES

In this note we provide a neccesary and sufficient condition for the non-emptiness of the socially stable core of a general structured TU-game which resembles closely the classical condition of balancedness given by Bondareva (1963) and Shapley (1967) to guarantee the non-emptiness of the classical core. Structured games have been introduced in Herings et al. (2007a) and more recently, in Herings et al. (2007b), studied in the framework of games with transferable utility. In the latter paper, the authors provide suffcient conditions for the non-emptiness of the socially stable core, but up to now, no necessary and sufficient condition is known.

Mixed and component wise condition numbers for weighted Moore-Penrose inverse and weighted least squares problems

Condition numbers play an important role in numerical analysis. Classical condition numbers are norm-wise: they measure both input perturbations and output errors with norms. To take into account the relative scaling of data components or a possible sparseness, component-wise condition numbers have been increasingly considered. In this paper, we give explicit expressions for the mixed and component-wise condition numbers for the weighted Moore-Penrose inverse of a matrix A, as well as for the solution and residue of a weighted linear least squares problem ||W 1 2 (Ax-b) ||2 = minv2Rn ||W 1 2 (Av-b) ||2, where the matrix A with full column rank. .