There has been significant progress in the study of sampling discretization of integral norms for both a designated finite-dimensional function space and a finite collection of such function spaces ...(universal discretization). Sampling discretization results turn out to be very useful in various applications, particularly in sampling recovery. Recent sampling discretization results typically provide existence of good sampling points for discretization. In this paper, we show that independent and identically distributed random points provide good universal discretization with high probability. Furthermore, we demonstrate that a simple greedy algorithm based on those points that are good for universal discretization provides excellent sparse recovery results in the square norm.
Resumen La proyección normativo-positivista de los derechos humanos es insuficiente para su garantía; por eso, para que estos derechos sean exigibles y cercanos a las personas, es pertinente la ...ampliación teórica del principio de universalidad y del concepto de garantía. En este sentido, más allá de lo que prescriben los sistemas domésticos y regionales para la exigibilidad de los derechos humanos, debemos aludir a la voz consuetus satisdatio que hace referencia a la garantía de los derechos en todo tiempo y lugar para la gestación de un auténtico control de universalidad de los derechos humanos.
A philosophical cause of universality and relevance in the acquisition of knowledge is annexed by the reality of inconsistency in the academic stadium. In essence, knowledge and by extension ...education is considered by universality as an essential substratum. It follows necessarily that knowledge which is an abstract reality is perceived to be universal, with minimal reference to particularity as the source of knowledge. Accordingly, when all variables are held constant, the acquisition of knowledge should be a form of a linear track which attracts the purview of particularity. This is why universality in the acquisition of knowledge is volatile due to inconsistencies caused by its nature in relation to acquisition of such knowledge in education theory and practice. Therefrom, this article delineates the cause-effect relationship of such discrepancy by emphasizing that there occurs extrication between the knower, the known, and the process of knowing. In this case, the knower is the recipient of knowledge, the known is the subject of knowledge, and the process of knowing is the modality of dispensing such knowledge.
Fibonacci family of dynamical universality classes Popkov, Vladislav; Schadschneider, Andreas; Schmidt, Johannes ...
Proceedings of the National Academy of Sciences - PNAS,
10/2015, Volume:
112, Issue:
41
Journal Article
Peer reviewed
Open access
Universality is a well-established central concept of equilibrium physics. However, in systems far away from equilibrium, a deeper understanding of its underlying principles is still lacking. Up to ...now, a few classes have been identified. Besides the diffusive universality class with dynamical exponentz= 2, another prominent example is the superdiffusive Kardar–Parisi–Zhang (KPZ) class withz= 3/2. It appears, e.g., in low-dimensional dynamical phenomena far from thermal equilibrium that exhibit some conservation law. Here we show that both classes are only part of an infinite discrete family of nonequilibrium universality classes. Remarkably, their dynamical exponentszα
are given by ratios of neighboring Fibonacci numbers, starting with eitherz₁ = 3/2 (if a KPZ mode exist) orz₁ = 2 (if a diffusive mode is present). If neither a diffusive nor a KPZ mode is present, all dynamical modes have the Golden Meanz= (1 + √5)/2 as dynamical exponent. The universal scaling functions of these Fibonacci modes are asymmetric Lévy distributions that are completely fixed by the macroscopic current density relation and compressibility matrix of the system and hence accessible to experimental measurement.
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Process-directed self-assembly refers to processes that reproducibly trap the kinetics of structure formation that ensues after a sudden change (“quench”) of the thermodynamic state ...into a desired, (meta)stable target state. This strategy benefits from specific advantages of copolymer systems, such as the rather comprehensive knowledge of equilibrium properties and the timescale separation between the quench of thermodynamic-state variables, the spontaneous relaxation of the system towards the “nearest” metastable state, and the thermally activated escape from the metastable target state. Particle-based and field-theoretic simulation techniques are reviewed and a selection of challenges for a quantitative prediction of processing of copolymer materials on the molecular scale are discussed.
Although detecting and characterizing community structure is key in the study of networked systems, we still do not understand how community structure affects systemic resilience and stability. We ...use percolation theory to develop a framework for studying the resilience of networks with a community structure. We find both analytically and numerically that interlinks (the connections among communities) affect the percolation phase transition in a way similar to an external field in a ferromagnetic– paramagnetic spin system. We also study universality class by defining the analogous critical exponents δ and γ, and we find that their values in various models and in real-world coauthor networks follow the fundamental scaling relations found in physical phase transitions. The methodology and results presented here facilitate the study of network resilience and also provide a way to understand phase transitions under external fields.
The present study investigated whether satisfaction and frustration of the psychological needs for autonomy, relatedness, and competence, as identified within Basic Psychological Need Theory (BPNT; ...Deci and Ryan, Psychol Inquiry 11:227–268,
2000
; Ryan and Deci, Psychol Inquiry 11:319–338,
2000
), contributes to participants’ well-being and ill-being, regardless of their cultural background and interpersonal differences in need strength, as indexed by either need valuation (i.e., the stated importance of the need to the person) or need desire (i.e., the desire to get a need met). In Study 1, involving late adolescents from Belgium and China (total
N
= 685; Mean age = 17 years), autonomy and competence satisfaction had unique associations with well-being and individual differences in need valuation did not moderate these associations. Study 2 involved participants from four culturally diverse nations (Belgium, China, USA, and Peru; total
N
= 1,051; Mean age = 20 years). Results provided evidence for the measurement equivalence of an adapted scale tapping into both need satisfaction and need frustration. Satisfaction of each of the three needs was found to contribute uniquely to the prediction of well-being, whereas frustration of each of the three needs contributed uniquely to the prediction of ill-being. Consistent with Study 1, the effects of need satisfaction and need frustration were found to be equivalent across the four countries and were not moderated by individual differences in the desire for need satisfaction. These findings underscore BPNT’s universality claim, which states that the satisfaction of basic needs for autonomy, relatedness, and competence represent essential nutrients for optimal functioning across cultures and across individual differences in need strength.
The intrinsic room-temperature ferromagnetism, stability in air, and easy tunability make chromium telluride Cr3Te4 a material with great promise for application in spintronics. This study ...investigates the magnetic entropy change (ΔSM) associated with critical exponents of Cr3Te4 single crystal. Temperature-dependent ΔSM suggests a drastic entropy change caused by the transition, the parameters of which show field-dependent power-law behaviors. Fitting the ΔSM(T,H) parameters yields critical exponents α=0.056(9), β=0.365(4), γ=1.212(3), δ=4.318(1), and Δ=1.562(5) for H//ab, while α=−0.077(3), β=0.369(6), γ=1.338(1), δ=4.620(6), and Δ=1.689(2) for H//c. The universality principle allows the ΔSM(T,H) to be scaled onto a single universal curve independent of external field. The direction-dependent differing critical exponents imply anisotropic magnetic couplings in Cr3Te4, which reveal a magnetic interaction of the 3D-Ising type for H//ab while a 3D-XY one for H//c. This work is beneficial for understanding the intrinsic and anisotropic room-temperature ferromagnetism in CrxTey family.
•The magnetic entropy change (ΔSM) of Cr3Te4 single crystal was investigated by the scaling method under the framework of universality principle.•The extracted parameters of ΔSM(T,H) fulfill the power-law dependent on H, the fitting of which gives reliable critical exponents.•With the critical exponents, the ΔSM(T,H) curves can be scaled onto a single universal curve due to the universality principal, revealing a magnetic interaction of the 3D-Ising type for H//ab while a 3D-XY one for H//c in Cr3Te4.
Universality in language has been a core issue in the fields of linguistics and psycholinguistics for many years (e.g., Chomsky, 1965). Recently, Frost (2012) has argued that establishing universals ...of process is critical to the development of meaningful, theoretically motivated, cross-linguistic models of reading. In contrast, other researchers argue that there is no such thing as universals of reading (e.g., Coltheart & Crain, 2012). Reading is a complex, visually mediated psychological process, and eye movements are the behavioural means by which we encode the visual information required for linguistic processing. To investigate universality of representation and process across languages we examined eye movement behaviour during reading of very comparable stimuli in three languages, Chinese, English and Finnish. These languages differ in numerous respects (character based vs. alphabetic, visual density, informational density, word spacing, orthographic depth, agglutination, etc.). We used linear mixed modelling techniques to identify variables that captured common variance across languages. Despite fundamental visual and linguistic differences in the orthographies, statistical models of reading behaviour were strikingly similar in a number of respects, and thus, we argue that their composition might reflect universality of representation and process in reading.
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