On the Power of Standard Information for Tractability for L2- Approximation in the Randomized Setting

We study the approximation of multivariate functions from a separable Hilbert space in the randomized setting with the error measured in the weighted L2 norm. We consider algorithms that use standard information Λstd consisting of function values or general linear information Λall consisting of arbitrary linear functionals. We investigate the equivalences of various notions of algebraic and exponential tractability in the randomized setting for Λstd and Λall for the normalized or absolute error criterion. For the normalized error criterion, we show that the power of Λstd is the same as that of Λall for all notions of exponential tractability and some notions of algebraic tractability without any condition. For the absolute error criterion, we show that the power of Λstd is the same as that of Λall for all notions of algebraic and exponential tractability without any condition. Specifically, we solve Open Problems 98, 101, 102 and almost solve Open Problem 100 as posed by E.Novak and H.Wo´zniakowski in the book: Tractability of Multivariate Problems, Volume III: Standard Information for Operators, EMS Tracts in Mathematics, Zürich, 2012.

One-Point Statistics Matter in Extended Cosmologies

The late universe contains a wealth of information about fundamental physics and gravity, wrapped up in non-Gaussian fields. To make use of as much information as possible it is necessary to go beyond two-point statistics. Rather than going to higher order N-point correlation functions, we demonstrate that the probability distribution function (PDF) of spheres in the matter field (a one-point function) already contains a significant amount of this non-Gaussian information. The matter PDF dissects different density environments which are lumped together in two-point statistics, making it particularly useful for probing modifications of gravity or expansion history. Our approach in Cataneo et. al. 2021 extends the success of Large Deviation Theory for predicting the matter PDF in ΛCDM in these “extended” cosmologies. A Fisher forecast demonstrates the information content in the matter PDF via constraints for a Euclid-like survey volume combining the 3D matter PDF with the 3D matter power spectrum. Adding the matter PDF halves the uncertainties on parameters in an evolving dark energy model, relative to the power spectrum alone. Additionally, the matter PDF contains enough non-linear information to substantially increase the detection significance of departures from General Relativity, with improvements up to six times the power spectrum alone. This analysis demonstrates that the matter PDF is a promising non-Gaussian statistic for extracting cosmological information, particularly for beyond ΛCDM models.

Heterochromatin Networks: Topology, Dynamics, and Function (a Working Hypothesis)

Open systems can only exist by self-organization as pulsing structures exchanging matter and energy with the outer world. This review is an attempt to reveal the organizational principles of the heterochromatin supra-intra-chromosomal network in terms of nonlinear thermodynamics. The accessibility of the linear information of the genetic code is regulated by constitutive heterochromatin (CHR) creating the positional information in a system of coordinates. These features include scale-free splitting-fusing of CHR with the boundary constraints of the nucleolus and nuclear envelope. The analysis of both the literature and our own data suggests a radial-concentric network as the main structural organization principle of CHR regulating transcriptional pulsing. The dynamic CHR network is likely created together with nucleolus-associated chromatin domains, while the alveoli of this network, including springy splicing speckles, are the pulsing transcription hubs. CHR contributes to this regulation due to the silencing position variegation effect, stickiness, and flexible rigidity determined by the positioning of nucleosomes. The whole system acts in concert with the elastic nuclear actomyosin network which also emerges by self-organization during the transcriptional pulsing process. We hypothesize that the the transcriptional pulsing, in turn, adjusts its frequency/amplitudes specified by topologically associating domains to the replication timing code that determines epigenetic differentiation memory.

The Role of Assumptions in Ohlson Model Performance: Lessons for Improving Equity-Value Modeling

In this paper, we test whether the short-run econometric conditions for the basic assumptions of the Ohlson valuation model hold, and then we relate these results with the fulfillment of the short-run econometric conditions for this model to be effective. Better future modeling motivated us to analyze to what extent the assumptions involved in this seminal model are not good enough approximations to solve the firm valuation problem, causing poor model performance. The model is based on the well-known dividend discount model and the residual income valuation model, and it adds a linear information model, which is a time series model by nature. Therefore, we adopt the time series approach. In the presence of non-stationary variables, we focus our research on US-listed firms for which more than forty years of data with the required cointegration properties to use error correction models are available. The results show that the clean surplus relation assumption has no impact on model performance, while the unbiased accounting property assumption has an important effect on it. The results also emphasize the uselessness of forcing valuation models to match the value displacement property of dividends.

Las Tics poder de pocos y alineación de muchos

Este artículo está bajo las perspectivas teóricas del constructivismo, del enfoque sociocultural y de la práctica deliberada. En él se plantea la importancia que tienen las Tics en el proceso de aprendizaje para la clasificación de los usuarios en tres categorías: novatos, iniciados y expertos. Descubrir el papel que juega la adquisición de estrategias y habilidades, así como también la motivación, para facilitar la implementación de tareas y/o solución de problemas. Puede ser a través de redes, grupos o individualmente, manifestado en un conocimiento declarativo y procedimental. Conclusión: Las Tics en su conjunto, presentan una información no lineal en múltiples y variadas formas, actualizada, diversos puntos de vista sobre la misma temática de una manera sincrónica, e introduce al usuario en un proceso interactivo, que le facilita la relación con otros conocimientos o con los propios, para aplicarlos en el momento oportuno en la realización de sus tareas. Estas reflexiones nos dan algunas pautas para pensar que si los estudiantes de las generaciones actuales y futuras ya son "novatos estratégicos" y poseen las competencias básicas de las Tics como mediadores instrumentales y culturales, debemos aprovechar esos conocimientos y caminar todos en ese mismo sentido. This trial is under the theoretical perspectives of constructivism, sociocultural approach and deliberate practice. Novices and experts started: in the importance of ICT in the learning process for classification of the subjects participating in three categories arises. How they operate in the acquisition of skills and strategies, the involvement of motivation and learning to facilitate of tasks and / or troubleshooting. It may be through networks, groups or individually, expressed in a declarative and procedural knowledge. Conclusion: ICT as a whole, have a non-linear information in many and varied forms, to date, different views on the same subject in a synchronous manner, and introduces the user in an interactive process that facilitates the relationship with other knowledge or own, to implement in a timely manner in carrying out their tasks. These reflections give us some guidelines to think that if students of present and future generations are already "strategic newbies" and possess the core competencies of ICTs as instrumental and cultural mediators, we must take all this knowledge and walk in the same direction.

Function Values Are Enough for $$L_2$$-Approximation

We study the $$L_2$$ L 2 -approximation of functions from a Hilbert space and compare the sampling numbers with the approximation numbers. The sampling number $$e_n$$ e n is the minimal worst-case error that can be achieved with n function values, whereas the approximation number $$a_n$$ a n is the minimal worst-case error that can be achieved with n pieces of arbitrary linear information (like derivatives or Fourier coefficients). We show that $$\begin{aligned} e_n \,\lesssim \, \sqrt{\frac{1}{k_n} \sum _{j\ge k_n} a_j^2}, \end{aligned}$$ e n ≲ 1 k n ∑ j ≥ k n a j 2 , where $$k_n \asymp n/\log (n)$$ k n ≍ n / log ( n ) . This proves that the sampling numbers decay with the same polynomial rate as the approximation numbers and therefore that function values are basically as powerful as arbitrary linear information if the approximation numbers are square-summable. Our result applies, in particular, to Sobolev spaces $$H^s_\mathrm{mix}(\mathbb {T}^d)$$ H mix s ( T d ) with dominating mixed smoothness $$s>1/2$$ s > 1 / 2 and dimension $$d\in \mathbb {N}$$ d ∈ N , and we obtain $$\begin{aligned} e_n \,\lesssim \, n^{-s} \log ^{sd}(n). \end{aligned}$$ e n ≲ n - s log sd ( n ) . For $$d>2s+1$$ d > 2 s + 1 , this improves upon all previous bounds and disproves the prevalent conjecture that Smolyak’s (sparse grid) algorithm is optimal.

AUTOMATION OF EVALUATION OF FACTOR RELATIONS AND STRATEGIES OF PRODUCTION AND TECHNOLOGICAL RELATIONS BY THE OPERATOR OF TRANSFORMATION OF THE BASIS OF LINEAR INFORMATION STRUCTURES

In this paper, an attempt is made to equivalent transformation of structured data by tabular forms by means of their adequate transformation into vector similarity forms, which significantly improve the conditions for formalization of computing processes and processing of information structures and data arrays. The solution of the problem is obtained by such a linear transformation of vector structures of information in the corresponding analytical dependencies using transformation matrices. The method of estimation of achievement of balance between expenses on the organization of production and, the income received from sale of production at the fixed price is offered.