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Journal articles on the topic 'Conditional Invariances'

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Author: Grafiati

Published: 10 December 2022

Last updated: 29 January 2023

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1

Joshi, Ameya, Minsu Cho, Viraj Shah, Balaji Pokuri, Soumik Sarkar, Baskar Ganapathysubramanian, and Chinmay Hegde. "InvNet: Encoding Geometric and Statistical Invariances in Deep Generative Models." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 04 (April 3, 2020): 4377–84. http://dx.doi.org/10.1609/aaai.v34i04.5863.

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Generative Adversarial Networks (GANs), while widely successful in modeling complex data distributions, have not yet been sufficiently leveraged in scientific computing and design. Reasons for this include the lack of flexibility of GANs to represent discrete-valued image data, as well as the lack of control over physical properties of generated samples. We propose a new conditional generative modeling approach (InvNet) that efficiently enables modeling discrete-valued images, while allowing control over their parameterized geometric and statistical properties. We evaluate our approach on several synthetic and real world problems: navigating manifolds of geometric shapes with desired sizes; generation of binary two-phase materials; and the (challenging) problem of generating multi-orientation polycrystalline microstructures.

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2

Krzysztofowicz, Roman, and Thomas A. Pomroy. "Disaggregative Invariance of Daily Precipitation." Journal of Applied Meteorology 36, no. 6 (June 1, 1997): 721–34. http://dx.doi.org/10.1175/1520-0450-36.6.721.

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Abstract Disaggregative invariance refers to stochastic independence between the total precipitation amount and its temporal disaggregation. This property is investigated herein for areal average and point precipitation amounts accumulated over a 24-h period and disaggregated into four 6-h subperiods. Statistical analyses of precipitation records from 1948 to 1993 offer convincing empirical evidence against the disaggregative invariance and in favor of the conditional disaggregative invariance, which arises when the total amount and its temporal disaggregation are conditioned on the timing of precipitation within the diurnal cycle. The property of conditional disaggregative invariance allows the modeler or the forecaster to decompose the problem of quantitative precipitation forecasting into three tasks: (i) forecasting the precipitation timing; (ii) forecasting the total amount, conditional on timing; and (iii) forecasting the temporal disaggregation, conditional on timing. Tasks (ii) and (iii) can be performed independently of one another, and this offers a formidable advantage for applications.

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3

de Palma, André, and Karim Kilani. "Invariance of conditional maximum utility." Journal of Economic Theory 132, no. 1 (January 2007): 137–46. http://dx.doi.org/10.1016/j.jet.2005.05.010.

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4

Burigana, Luigi, and Michele Vicovaro. "“Invariants” in Koffka’s Theory of Constancies in Vision: Highlighting Their Logical Structure and Lasting Value." Gestalt Theory 39, no. 1 (March 1, 2017): 6–29. http://dx.doi.org/10.1515/gth-2017-0004.

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SummaryBy introducing the concept of “invariants”, Koffka (1935) endowed perceptual psychology with a flexible theoretical tool, which is suitable for representing vision situations in which a definite part of the stimulus pattern is relevant but not sufficient to determine a corresponding part of the perceived scene. He characterised his “invariance principle” as a principle conclusively breaking free from the “old constancy hypothesis”, which rigidly surmised point-to-point relations between stimulus and perceptual properties. In this paper, we explain the basic terms and assumptions implicit in Koffka’s concept, by representing them in a set-theoretic framework. Then, we highlight various aspects and implications of the concept in terms of answers to six separate questions: forms of invariants, heuristic paths to them, what is invariant in an invariant, roots of conditional indeterminacy, variability vs. indeterminacy, and overcoming of the indeterminacy. Lastly, we illustrate the lasting value and theoretical power of the concept, by showing that Koffka’s insights relating to it do occur in modern perceptual psychology and by highlighting its role in a model of perceptual transparency.

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5

van Putten, C., and J. H. van Schuppen. "Invariance Properties of the Conditional Independence Relation." Annals of Probability 13, no. 3 (August 1985): 934–45. http://dx.doi.org/10.1214/aop/1176992915.

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6

Fushchich, V. I., and N. I. Serov. "Conditional invariance of the nonlinear wave equation." Ukrainian Mathematical Journal 43, no. 4 (April 1991): 359–64. http://dx.doi.org/10.1007/bf01670077.

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7

Fushchich, V. I., and N. I. Serov. "Conditional invariance of the nonlinear wave equation." Ukrainian Mathematical Journal 43, no. 3 (March 1991): 359–64. http://dx.doi.org/10.1007/bf01060847.

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8

Poryvai, D. V. "An invariance principle for conditional empirical processes." Russian Mathematical Surveys 59, no. 5 (October 31, 2004): 971–72. http://dx.doi.org/10.1070/rm2004v059n05abeh000783.

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9

Yehorchenko, I. A. "Differential Invariants, Hidden and Conditional Symmetry." Ukrainian Mathematical Journal 73, no. 8 (January 2022): 1189–99. http://dx.doi.org/10.1007/s11253-022-01986-7.

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10

Pruss, Alexander R. "Two Kinds of Invariance of Full Conditional Probabilities." Bulletin of the Polish Academy of Sciences Mathematics 61, no. 3 (2013): 277–83. http://dx.doi.org/10.4064/ba61-3-9.

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11

Nogales, A. G., and J. A. Oyola. "Some remarks on sufficiency, invariance and conditional independence." Annals of Statistics 24, no. 2 (April 1996): 906–9. http://dx.doi.org/10.1214/aos/1032894473.

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12

INAL, Hatice, and ,Duygu ANIL. "Investigation of Group Invariance in Test Equating Under Different Simulation Conditions." Eurasian Journal of Educational Research 18, no. 78 (November 29, 2018): 1–20. http://dx.doi.org/10.14689/ejer.2018.78.4.

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13

Jung, Eunju, and Yongjin Lee. "College Students’ Entrepreneurial Mindset: Educational Experiences Override Gender and Major." Sustainability 12, no. 19 (October 8, 2020): 8272. http://dx.doi.org/10.3390/su12198272.

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Entrepreneurship education has been popularly adopted in higher education contexts. Although evidence-based implementations of such education are widely acknowledged as beneficial, valid assessments of it are sparse. One possible outcome of entrepreneurship education is a change in students’ entrepreneurial mindset, which can be measured by the recently validated College Students’ Entrepreneurial Mindset Scale (CS-EMS). However, this scale awaits evidence regarding measurement invariance. This study aims to (1) examine measurement invariance of the CS-EMS; (2) compare the latent and observed means across groups based on gender, major, and educational experiences; and (3) investigate the conditional effects of the three grouping variables. Using data from 317 Korean college students’ survey responses, we conducted sequential tests of factorial invariance and latent mean comparisons using multiple-group confirmatory factor analysis. Additionally, the conditional effects of the gender, major, and educational experiences were tested by structural equation modeling. The results indicate that strict invariance held for the groups compared by either gender or educational experiences, while scalar invariance held between the engineering and non-engineering groups. While the male, engineering, and educational experience groups generally scored higher on both the latent and observed sub-scales, the results of the conditional effects of grouping variables indicated that educational experiences mattered most. One practical implication for the educators is that the CS-EMS is a promising assessment tool for addressing the effectiveness of entrepreneurship education, especially when the targeted educational goals are any of its sub-constructs.

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14

Conte, G., A. M. Perdon, E. Zattoni, and C. H. Moog. "Invariance, controlled invariance and conditioned invariance in structured systems and applications to disturbance decoupling." IOP Conference Series: Materials Science and Engineering 707 (December 9, 2019): 012010. http://dx.doi.org/10.1088/1757-899x/707/1/012010.

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15

Pollett, P. K. "Reversibility, invariance and μ-invariance." Advances in Applied Probability 20, no. 3 (September 1988): 600–621. http://dx.doi.org/10.2307/1427037.

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In this paper we consider a number of questions relating to the problem of determining quasi-stationary distributions for transient Markov processes. First we find conditions under which a measure or vector that is µ-invariant for a matrix of transition rates is also μ-invariant for the family of transition matrices of the minimal process it generates. These provide a means for determining whether or not the so-called stationary conditional quasi-stationary distribution exists in the λ-transient case. The process is not assumed to be regular, nor is it assumed to be uniform or irreducible. In deriving the invariance conditions we reveal a relationship between μ-invariance and the invariance of measures for related processes called the μ-reverse and the μ-dual processes. They play a role analogous to the time-reverse process which arises in the discussion of stationary distributions. Secondly we bring the related notions of detail-balance and reversibility into the realm of quasi-stationary processes. For example, if a process can be identified as being μ-reversible, the problem of determining quasi-stationary distributions is made much simpler. Finally, we consider some practical problems that emerge when calculating quasi-stationary distributions directly from the transition rates of the process. Our results are illustrated with reference to a variety of processes including examples of birth and death processes and the birth, death and catastrophe process.

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16

Pollett, P. K. "Reversibility, invariance and μ-invariance." Advances in Applied Probability 20, no. 03 (September 1988): 600–621. http://dx.doi.org/10.1017/s0001867800018164.

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In this paper we consider a number of questions relating to the problem of determining quasi-stationary distributions for transient Markov processes. First we find conditions under which a measure or vector that is µ-invariant for a matrix of transition rates is also μ-invariant for the family of transition matrices of the minimal process it generates. These provide a means for determining whether or not the so-called stationary conditional quasi-stationary distribution exists in the λ-transient case. The process is not assumed to be regular, nor is it assumed to be uniform or irreducible. In deriving the invariance conditions we reveal a relationship between μ-invariance and the invariance of measures for related processes called the μ-reverse and the μ-dual processes. They play a role analogous to the time-reverse process which arises in the discussion of stationary distributions. Secondly we bring the related notions of detail-balance and reversibility into the realm of quasi-stationary processes. For example, if a process can be identified as being μ-reversible, the problem of determining quasi-stationary distributions is made much simpler. Finally, we consider some practical problems that emerge when calculating quasi-stationary distributions directly from the transition rates of the process. Our results are illustrated with reference to a variety of processes including examples of birth and death processes and the birth, death and catastrophe process.

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17

Myronyk, Pavlo, and Natalia Bubenchikova. "Conditional Invariance and Exact Solutions of a Nonlinear System." Journal of Nonlinear Mathematical Physics 4, no. 1-2 (January 1997): 114–16. http://dx.doi.org/10.2991/jnmp.1997.4.1-2.14.

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18

Serov, N. I. "Conditional invariance and exact solutions of the nonlinear equation." Ukrainian Mathematical Journal 42, no. 10 (October 1990): 1216–22. http://dx.doi.org/10.1007/bf01057392.

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19

COLONIUS, FRITZ. "Metric invariance entropy and conditionally invariant measures." Ergodic Theory and Dynamical Systems 38, no. 3 (October 20, 2016): 921–39. http://dx.doi.org/10.1017/etds.2016.72.

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Two notions of metric invariance entropy are constructed with respect to conditionally invariant measures for control systems in discrete time and it is shown that they are invariant under conjugacies.

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20

Schütz, Gunter M. "Conformal invariance in conditioned stochastic particle systems." Journal of Physics A: Mathematical and Theoretical 50, no. 31 (July 7, 2017): 314002. http://dx.doi.org/10.1088/1751-8121/aa7ab2.

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21

Hein, Vello, Arunas Emeljanovas, and Brigita Mieziene. "A cross-cultural validation of the controlling teacher behaviours scale in physical education." European Physical Education Review 24, no. 2 (December 9, 2016): 209–24. http://dx.doi.org/10.1177/1356336x16681821.

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The present study examined the validity of the factor structure and invariance of the Controlling Teacher Behaviours Scale (CTBS) across two nations. Data were collected from Estonian ( n=453) and Lithuanian ( n=431) students using the multidimensional measure of teachers’ controlling behaviours. Multi-sample confirmatory factor analyses showed that the measure of teachers’ controlling behaviours with four scales (negative conditional regard, controlling use of rewards, excessive personal control and intimidation) were partially invariant at the configural, metric and strong invariance level. The results of the latent mean estimates showed no differences between Estonian and Lithuanian students in respect of the perception of the use of reward, whereas the perception of negative conditional regard, intimidation and excessive personal control appeared to be higher for Estonian students. The results indicated that CTBS is generally suitable for measuring the perceptions of teachers’ controlling behaviour among Estonian and Lithuanian students. Furthermore, results established that one item was perceived differently across samples and, therefore, there is a need for further research to test the invariance of the CTBS among student samples with different cultural backgrounds.

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22

CRYTSER, DANNY, and GABRIEL NAGY. "TRACES ARISING FROM REGULAR INCLUSIONS." Journal of the Australian Mathematical Society 103, no. 2 (November 3, 2016): 190–230. http://dx.doi.org/10.1017/s1446788716000501.

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We study the problem of extending a state on an abelian $C^{\ast }$-subalgebra to a tracial state on the ambient $C^{\ast }$-algebra. We propose an approach that is well suited to the case of regular inclusions, in which there is a large supply of normalizers of the subalgebra. Conditional expectations onto the subalgebra give natural extensions of a state to the ambient $C^{\ast }$-algebra; we prove that these extensions are tracial states if and only if certain invariance properties of both the state and conditional expectations are satisfied. In the example of a groupoid $C^{\ast }$-algebra, these invariance properties correspond to invariance of associated measures on the unit space under the action of bisections. Using our framework, we are able to completely describe the tracial state space of a Cuntz–Krieger graph algebra. Along the way we introduce certain operations called graph tightenings, which both streamline our description and provide connections to related finiteness questions in graph $C^{\ast }$-algebras. Our investigation has close connections with the so-called unique state extension property and its variants.

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23

Breier, P. "Local limit theorems for functionals in the conditional invariance principle." Journal of Soviet Mathematics 43, no. 6 (December 1988): 2764–68. http://dx.doi.org/10.1007/bf01129889.

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24

Janowicz, Maciej, and Andrzej Zembrzuski. "Symmetry Properties of Modified Black-Scholes Equation." Metody Ilościowe w Badaniach Ekonomicznych 22, no. 2 (May 17, 2022): 77–86. http://dx.doi.org/10.22630/mibe.2021.22.2.7.

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This paper concerns the classical and conditional symmetries of the Black-Scholes equation. Modifications of the Black-Scholes equation have also been considered and their maximal algebras of invariance have been found. Examples of creation operators for the Black-Scholes eigenvalue problem have been provided.

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25

LePage, Raoul, Krzysztof Podgórski, and Michał Ryznar. "Strong and conditional invariance principles for samples attracted to stable laws." Probability Theory and Related Fields 108, no. 2 (June 4, 1997): 281–98. http://dx.doi.org/10.1007/s004400050110.

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26

Peligrad, Magda, and Sergey Utev. "On the invariance principle for reversible Markov chains." Journal of Applied Probability 53, no. 2 (June 2016): 593–99. http://dx.doi.org/10.1017/jpr.2016.23.

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Abstract In this paper we investigate the functional central limit theorem (CLT) for stochastic processes associated to partial sums of additive functionals of reversible Markov chains with general spate space, under the normalization standard deviation of partial sums. For this case, we show that the functional CLT is equivalent to the fact that the variance of partial sums is regularly varying with exponent 1 and the partial sums satisfy the CLT. It is also equivalent to the conditional CLT.

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27

Grundland, A. M., and B. Huard. "Conditional symmetries and Riemann invariants for hyperbolic systems of PDEs." Journal of Physics A: Mathematical and Theoretical 40, no. 15 (March 23, 2007): 4093–123. http://dx.doi.org/10.1088/1751-8113/40/15/004.

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28

Grundland, A. M., and B. Huard. "Conditional symmetries and Riemann invariants for inhomogeneous hydrodynamic-type systems." Journal of Physics A: Mathematical and Theoretical 43, no. 45 (October 25, 2010): 455217. http://dx.doi.org/10.1088/1751-8113/43/45/455217.

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29

CHAKRABARTI, BARNALI, and TAPAN KUMAR DAS. "CONDITIONALLY EXACTLY SOLVABLE SINGULAR EVEN POWER POTENTIAL IN SUPERSYMMETRIC QUANTUM MECHANICS." Modern Physics Letters A 17, no. 21 (July 10, 2002): 1367–75. http://dx.doi.org/10.1142/s0217732302007375.

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We solve strongly singular even power potential with inverse quadratic, inverse quartic and inverse sextic terms, using superpotential ansatz technique. We show that our new technique is very powerful and simple compared to traditional wave function ansatz technique. We also point out conditional shape invariance as the underlying symmetry to get conditional exactness. We also generalize the case for two-body Hamiltonian and propose an alternative way to solve Riccati equation instead of solving Schrödinger equation. We present operator formalism which is rather powerful. We also discuss the problem encountered in generalizing the potential for an N-body system.

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30

Andiarti, R., and C. H. Moog. "The Role of Conditioned Invariance in Generalized Nonlinear Observers." IFAC Proceedings Volumes 29, no. 1 (June 1996): 2156–61. http://dx.doi.org/10.1016/s1474-6670(17)57991-4.

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31

Caravenna, Francesco, and Loïc Chaumont. "Invariance principles for random walks conditioned to stay positive." Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 44, no. 1 (February 2008): 170–90. http://dx.doi.org/10.1214/07-aihp119.

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32

Poryvai, D. V. "The invariance principle for conditional empirical processes formed by dependent random variables." Izvestiya: Mathematics 69, no. 4 (August 31, 2005): 771–89. http://dx.doi.org/10.1070/im2005v069n04abeh001662.

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33

Vaněček, A. "Controlled and conditioned invariants in linear system theory." Automatica 30, no. 2 (February 1994): 369–70. http://dx.doi.org/10.1016/0005-1098(94)90042-6.

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34

Koo, Ja Kyung, and Dong Sung Yoon. "On the Schertz Conjecture." Proceedings of the Edinburgh Mathematical Society 62, no. 3 (February 8, 2019): 837–45. http://dx.doi.org/10.1017/s0013091518000895.

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AbstractSchertz conjectured that every finite abelian extension of imaginary quadratic fields can be generated by the norm of the Siegel–Ramachandra invariants. We present a conditional proof of his conjecture by means of the characters on class groups and the second Kronecker limit formula.

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35

Özkan, Batuhan, and Fatma Noyan Tekeli. "THE EFFECTS OF INFORMATION AND COMMUNICATION TECHNOLOGY ENGAGEMENT FACTORS ON SCIENCE PERFORMANCE BETWEEN SINGAPORE AND TURKEY USING MULTI-GROUP STRUCTURAL EQUATION MODELING." Journal of Baltic Science Education 20, no. 4 (August 15, 2021): 639–50. http://dx.doi.org/10.33225/jbse/21.20.639.

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Information and Communication Technology (ICT) engagement, as a multidimensional construct, plays an increasingly important role in education. The main purpose of this research was to explore the effects of ICT engagement factors on science performance across Singapore and Turkey conditional to the sufficient degree of measurement invariance of ICT engagement scale. The multi-group confirmatory factor analysis results demonstrated strong factorial invariance of ICT engagement scale across Singapore and Turkey, so we were able to use ICT engagement scale to meaningful and valid comparisons between these countries. After obtaining measurement invariance, a multi-group structural equation modeling was used for the comparison of the effects of ICT engagement factors on student’s performance of science between these two countries. While interest in ICT, perceived ICT competence and perceived autonomy in using ICT have significant positive direct effect on science performance in both countries, the direct effect of social relatedness in using ICT on science performance is negative in both Singapore and Turkey. Also, when compared with Singapore, the effects of all ICT engagement constructs on student’s performance are higher in Turkey. Keywords: ICT engagement, measurement invariance, multi-group SEM, science performance, PISA 2018

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36

Shaker, Ammar, Shujian Yu, and Daniel Oñoro-Rubio. "Learning to Transfer with von Neumann Conditional Divergence." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 8 (June 28, 2022): 8231–39. http://dx.doi.org/10.1609/aaai.v36i8.20797.

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The similarity of feature representations plays a pivotal role in the success of problems related to domain adaptation. Feature similarity includes both the invariance of marginal distributions and the closeness of conditional distributions given the desired response y (e.g., class labels). Unfortunately, traditional methods always learn such features without fully taking into consideration the information in y, which in turn may lead to a mismatch of the conditional distributions or the mixup of discriminative structures underlying data distributions. In this work, we introduce the recently proposed von Neumann conditional divergence to improve the transferability across multiple domains. We show that this new divergence is differentiable and eligible to easily quantify the functional dependence between features and y. Given multiple source tasks, we integrate this divergence to capture discriminative information in y and design novel learning objectives assuming those source tasks are observed either simultaneously or sequentially. In both scenarios, we obtain favorable performance against state-of-the-art methods in terms of smaller generalization error on new tasks and less catastrophic forgetting on source tasks (in the sequential setup).

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37

Gavalakis, Lampros, and Ioannis Kontoyiannis. "Sharp Second-Order Pointwise Asymptotics for Lossless Compression with Side Information." Entropy 22, no. 6 (June 25, 2020): 705. http://dx.doi.org/10.3390/e22060705.

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The problem of determining the best achievable performance of arbitrary lossless compression algorithms is examined, when correlated side information is available at both the encoder and decoder. For arbitrary source-side information pairs, the conditional information density is shown to provide a sharp asymptotic lower bound for the description lengths achieved by an arbitrary sequence of compressors. This implies that for ergodic source-side information pairs, the conditional entropy rate is the best achievable asymptotic lower bound to the rate, not just in expectation but with probability one. Under appropriate mixing conditions, a central limit theorem and a law of the iterated logarithm are proved, describing the inevitable fluctuations of the second-order asymptotically best possible rate. An idealised version of Lempel-Ziv coding with side information is shown to be universally first- and second-order asymptotically optimal, under the same conditions. These results are in part based on a new almost-sure invariance principle for the conditional information density, which may be of independent interest.

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38

Chu, You-Biao, and Xi-Yun Lu. "Topological evolution in compressible turbulent boundary layers." Journal of Fluid Mechanics 733 (September 23, 2013): 414–38. http://dx.doi.org/10.1017/jfm.2013.399.

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AbstractTopological evolution of compressible turbulent boundary layers at Mach 2 is investigated by means of statistical analysis of the invariants of the velocity gradient tensor based on the direct numerical simulation database. The probability density functions of the rate of change of the invariants exhibit the $- 3$ power-law distribution in the region of large Lagrangian derivative of the invariants in the inner and outer layers. The topological evolution is studied by conditional mean trajectories for the evolution of the invariants. The trajectories illustrate inward-spiralling orbits around and converging to the origin of the space of invariants in the outer layer, while they are repelled by the vicinity of the origin and converge towards a limit cycle in the inner layer. The compressibility effect on the mean topological evolution is studied in terms of the ‘incompressible’, compressed and expanding regions. It is found that the mean evolution of flow topologies is altered by the compressibility. The evolution equations of the invariants are derived and the relevant dynamics of the mean topological evolution are analysed. The compressibility effect is mainly related to the pressure effect. The mutual-interaction terms among the invariants are the root of the clockwise spiral behaviour of the local flow topology in the space of invariants.

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39

Zaîtsev, A. Yu. "Estimates for the quantiles of smooth conditional distributions and the multidimensional invariance principle." Siberian Mathematical Journal 37, no. 4 (July 1996): 706–29. http://dx.doi.org/10.1007/bf02104663.

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40

Zbinden, Rainer, Christian Wollmann, Johannes Brachmann, Jochen Michaelsen, Clemens Steinwender, Pramesh Kovoor, Sebastian Kelle, et al. "Clinical safety of the ProMRI implantable cardioverter-defibrillator systems during head and lower lumbar magnetic resonance imaging at 3 T: results of the ProMRI 3T ENHANCED Master study." EP Europace 21, no. 11 (July 19, 2019): 1678–85. http://dx.doi.org/10.1093/europace/euz189.

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Abstract Aims There have been no published studies on the safety of magnetic resonance imaging (MRI) at 3 Tesla (3 T) in patients with MRI-conditional implantable cardioverter-defibrillators (ICDs). The aim of this study was to assess clinical safety of the Biotronik ProMRI ICD system during non-diagnostic head and lower lumbar scans under 3 T MRI conditions. Methods and results The study enrolled 129 patients at 12 sites in Australia, Singapore, and Europe. Predefined head and lower lumbar MR scans (total duration ≈30 min) were performed in 112 patients. Three primary endpoints were evaluated from the pre-MRI to the 1-month post-MRI visit: (i) freedom from serious adverse device effects (SADEs) related to MRI (hypothesized to be >90%); (ii) pacing threshold invariance for all leads (geometric mean of the patient-wise ratios for 1 month vs. pre-MRI was hypothesized to be <1.07); and (iii) sensing amplitude invariance (geometric mean of the ratios was hypothesized to be >0.993). No MRI-related SADE occurred (SADE-free rate 100%, 95% confidence interval 95.98–100%). Pacing threshold and sensing amplitudes fulfilled the invariance hypotheses with high statistical significance (P < 0.0013). No threshold increase >0.5 V or sensing amplitude decrease by >50% was observed (secondary endpoints). Lead impedances, battery capacity, and detection and treatment of arrhythmias by ICDs were not affected by MRI scans. Conclusion The head and lower lumbar scans under specific 3 T MRI conditions were safe in the investigated MR-conditional ICD systems. There was no evidence of harm to the patients or any negative influence of the MRI scan on the implanted systems.

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41

Otsuka, Naohisa. "Generalized controlled and conditioned invariances for linear ω-periodic discrete-time systems." Linear Algebra and its Applications 327, no. 1-3 (April 2001): 207–23. http://dx.doi.org/10.1016/s0024-3795(00)00309-8.

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42

Gitelman, Alix I. "Estimating Causal Effects From Multilevel Group-Allocation Data." Journal of Educational and Behavioral Statistics 30, no. 4 (December 2005): 397–412. http://dx.doi.org/10.3102/10769986030004397.

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In group-allocation studies for comparing behavioral, social, or educational interventions, subjects in the same group necessarily receive the same treatment, whereby a group and/or group-dynamic effect can confound the treatment effect. General counterfactual outcomes that depend on group characteristics, group membership, and treatment are developed to provide a structure for specifying causal effects of treatment in the multilevel setting. An average causal effect of treatment cannot be specified, however, without a simplifying assumption of group-membership invariance (i.e., no group-dynamic effect). Under group-membership invariance and ignorability assumptions, the average causal effect is then connected to estimable quantities of the hierarchical linear model (HLM). Furthermore, it is shown that the typical specification of the HLM involves conditional independence assumptions that actually preclude the group-dynamic effect.

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43

KATOK, A., and R. J. SPATZIER. "Corrections to ‘Invariant measures for higher-rank hyperbolic abelian actions’." Ergodic Theory and Dynamical Systems 18, no. 2 (April 1998): 503–7. http://dx.doi.org/10.1017/s0143385798110969.

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The proofs of Theorems 5.1 and 7.1 of [2] contain a gap. We will show below how to close it under some suitable additional assumptions in these theorems and their corollaries. We will assume the notation of [2] throughout. In particular, $\mu$ is a measure invariant and ergodic under an $R^k$-action $\alpha$. Let us first explain the gap. Both theorems are proved by establishing a dichotomy for the conditional measures of $\mu$ along the intersection of suitable stable manifolds. They were either atomic or invariant under suitable translation or unipotent subgroups $U$. Atomicity eventually led to zero entropy. Invariance of the conditional measures showed invariance of $\mu$ under $U$. We then claimed that $\mu$ was algebraic using, respectively, unique ergodicity of the translation subgroup on a rational subtorus or Ratner's theorem (cf. [2, Lemma 5.7]). This conclusion, however, only holds for the $U$-ergodic components of $\mu$ which may not equal $\mu$. In fact, in the toral case, the $R^k$-action may have a zero-entropy factor such that the conditional measures along the fibers are Haar measures along a foliation by rational subtori. Since invariant measures with zero entropy have not been classified, we cannot conclude algebraicity of the total measure $\mu$ at this time. In the toral case, the existence of zero entropy factors turns out to be precisely the obstruction to our methods. The case of Weyl chamber flows is somewhat different as the ‘Haar’ direction of the measure may not be integrable. In this case, we need to use additional information coming from the semisimplicity of the ambient Lie group to arrive at the versions of Theorem 7.1 presented below.

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Lipovetzky, Nir, Christian Muise, and Hector Geffner. "Traps, Invariants, and Dead-Ends." Proceedings of the International Conference on Automated Planning and Scheduling 26 (March 30, 2016): 211–15. http://dx.doi.org/10.1609/icaps.v26i1.13774.

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We consider the problem of deriving formulas that capture traps, invariants, and dead-ends in classical planning through polynomial forms of preprocessing. An invariant is a formula that is true in the initial state and in all reachable states. A trap is a conditional invariant: once a state is reached that makes the trap true, all the states that are reachable from it will sat- isfy the trap formula as well. Finally, dead-ends are formulas that are satisfied in states that make the goal unreachable. We introduce a preprocessing algorithm that computes traps in k- DNF form that is exponential in the k parameter, and show how the algorithm can be used to precompute invariants and dead-ends. We report also preliminary tests that illustrate the effectiveness of the preprocessing algorithm for identifying dead-end states, and compare it with the identification that follows from the use of the h1 and h2 heuristics that cannot be preprocessed, and must be computed at run time.

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Qu, Changzheng, Lina Ji, and Lizhen Wang. "Conditional Lie Bäcklund Symmetries and Sign-Invariants to Quasi-Linear Diffusion Equations." Studies in Applied Mathematics 119, no. 4 (October 1, 2007): 355–91. http://dx.doi.org/10.1111/j.1467-9590.2007.00388.x.

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Ji, Lina, Xiangwei Zhang, and Rong Yan. "Conditional Lie–Bäcklund symmetries and sign-invariants to second-order evolution equations." Communications in Nonlinear Science and Numerical Simulation 17, no. 9 (September 2012): 3476–82. http://dx.doi.org/10.1016/j.cnsns.2012.01.011.

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Qasim, Tahira Bano, Hina Ali, Natasha Malik, and Malika Liaquat. "Forecasting Inflation Applying ARIMA Model with GARCH Innovation: The Case of Pakistan." Journal of Accounting and Finance in Emerging Economies 7, no. 2 (June 30, 2021): 305–16. http://dx.doi.org/10.26710/jafee.v7i2.1681.

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Purpose: The research aims to build a suitable model for the conditional mean and conditional variance for forecasting the rate of inflation in Pakistan by summarizing the properties of the series and characterizing its salient features. Design/Methodology/Approach: For this purpose, Pakistan’s Inflation Rate is based upon the Consumer Price Index (CPI), ranging from January 1962 to December 2019 has been analyzed. Augmented Dickey Fuller (ADF) test that was used for testing the stationarity of the series. The ARIMA modeling technique is a conditional mean and GARCH model for conditional variance. Models are selected on AIC and BIC model selection criteria. The estimating and forecasting ability of three ARIMA models with the GARCH (2,2) model has been compared to capture the possible nonlinearity present in the data. To depict the possible asymmetric effect in the conditional variance, two asymmetric GARCH models, EGARCH and TGARCH models have been applied. Findings: Based on statistical loss functions, GARCH (2,2) model is the best variance model for this series. The empirical results reveal that the performance of model-2 is best for all the three variance models. However, the GARCH model is the best as the variance model for this series. This shows that the asymmetric effect invariance is not so important for the rate of inflation in Pakistan. Implications/Originality/Value: The current study was based on the least considered variables and the pioneer in testing the complex relationship through the ARIMA model with GARCH innovation.

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Gaeta, Giuseppe, Roma Kozlov, and Francesco Spadaro. "Asymptotic symmetry and asymptotic solutions to Ito stochastic differential equations." Mathematics in Engineering 4, no. 5 (2022): 1–52. http://dx.doi.org/10.3934/mine.2022038.

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<abstract><p>We consider several aspects of conjugating symmetry methods, including the method of invariants, with an asymptotic approach. In particular we consider how to extend to the stochastic setting several ideas which are well established in the deterministic one, such as conditional, partial and asymptotic symmetries. A number of explicit examples are presented.</p></abstract>

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Buchek, A. A., and A. V. Ermolenko. "ACMEOLOGICAL INVARIANTS OF PROFESSIONALISM: STATEMENT OF THE PROBLEM." Bulletin of Kemerovo State University, no. 2 (July 8, 2016): 73–76. http://dx.doi.org/10.21603/2078-8975-2016-2-73-76.

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The paper contains the results of the theoretical analysis of the problem of personal and professional development of the heads of educational institutions. The authors of the work describe and analyze the features of acmeological invariants of professionalism as regulators of the successful achievement of professional development. The authors intend to do the study of acmeological invariants through the analysis of subsystems of professionalism conditioned by the specifics of activity of the heads of educational institutions.

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Trifonov, Ju S., and B. S. Potanin. "Multivariate Asymmetric GARCH Model with Dynamic Correlation Matrix." Finance: Theory and Practice 26, no. 2 (April 29, 2022): 204–18. http://dx.doi.org/10.26794/2587-5671-2022-26-2-204-218.

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This study examines the problem of modeling the joint dynamics of conditional volatility of several financial assets under an asymmetric relationship between volatility and shocks in returns (leverage effect). We propose a new multivariate asymmetric conditional heteroskedasticity model with a dynamic conditional correlation matrix (DCC-EGARCH). The proposed method allows modelling the joint dynamics of several financial assets taking into account the leverage effect in the financial markets. DCC-EGARCH model has two main advantages over previously proposed multivariate asymmetric specifications. It involves a substantially simpler optimization problem and does away with the assumption of conditional correlation time invariance. These features make the model more suitable for practical applications. To study the properties of the obtained estimators, we conducted a simulated data analysis. As a result, we found statistical evidence in favor of the developed DCC-EGARCH model compared with the symmetric DCC-GARCH process in case of considering data with the presence of the leverage effect. Further, we applied the proposed method to analyze the joint volatility of Rosneft stock returns and Brent oil prices. By estimating the DCC-EGARCH model, we found statistical evidence for both the presence of the leverage effect in the oil price data and the presence of the dynamic correlation structure between the time series, which motivates the practical application of the proposed method.

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