Mathematically, gauge theories are extraordinarily rich --- so rich, in fact, that it can become all too easy to lose track of the connections between results, and become lost in a mass of beautiful theorems and properties: indeterminism, constraints, Noether identities, local and global symmetries, and so on. -/- One purpose of this short article is to provide some sort of a guide through the mathematics, to the conceptual core of what is actually going on. Its focus is on the (...) Lagrangian, variational-problem description of classical mechanics, from which the link between gauge symmetry and the apparent violation of determinism is easy to understand; only towards the end will the Hamiltonian description be considered. -/- The other purpose is to warn against adopting too unified a perspective on gauge theories. It will be argued that the meaning of the gauge freedom in a theory like general relativity is (at least from the Lagrangian viewpoint) significantly different from its meaning in theories like electromagnetism. The Hamiltonian framework blurs this distinction, and orthodox methods of quantization obliterate it; this may, in fact, be genuine progress, but it is dangerous to be guided by mathematics into conflating two conceptually distinct notions without appreciating the physical consequences. (shrink)

We investigate the long-term evolution of degree-degree correlations (assortativity) in functional brain networks from epilepsy patients. Functional networks are derived from continuous multi-day, multi-channel electroencephalographic data, which capture a wide range of physiological and pathophysiological activities. In contrast to previous studies which all reported functional brain networks to be assortative on average, even in case of various neurological and neurodegenerative disorders, we observe large fluctuations in time-resolved degree-degree correlations ranging from assortative to dissortative mixing. Moreover, in some patients these (...) fluctuations exhibit some periodic temporal structure which can be attributed, to a large extent, to daily rhythms. Relevant aspects of the epileptic process, particularly possible pre-seizure alterations, contribute marginally to the observed long-term fluctuations. Nevertheless, our findings suggest that physiological and pathophysiological activity may modify functional brain networks in a different and process-specific way. We evaluate factors that possibly influence the long-term evolution of degree-degree correlations. (shrink)

Compound propositions which can successfully be defended in a quantumdialogue independent of the elementary propositions contained in it, must have this property also independent of the mutual elementary commensur-abilities. On the other hand, formal commensurabilities must be taken into account. Therefore, for propositions which can be proved by P, irrespective of both the elementary propositions and of the elementary commensur-abilities, there exists a formal strategy of success. The totality of propositions with a formal strategy of success in a quantum dialogue (...) form the effective quantum logic. The propositions of the effective quantum logic can be derived from a calculus Q eff which is — on the other hand — equivalent to a lattice L qi.Propositions about measuring results are above all time dependent propositions A(S;t). In a dialogue, different partial propositions will have in general different time values. If one can (accidentally) win a material dialogue, this dialogue can be related to a single time value. For the propositions of the effective quantum logic there exist formal strategies of success, independent of the elementary propositions contained in it. All partial propositions appearing in the dialogue are formally commensurable. Therefore the propositions of effective quantum logic which can be proved by formal dialogues can always be related to a single time. They present a description of the system S considered in which all partial propositions can be related jointly to the state of S.Therefore in the effective quantum logic we have — in the limit of equal time values — a situation which corresponds conceptually to the description of the system (S; ψ) in Hilbert space. Consequently, one would expect that also the lattice L qi — except from the tertium non datur 8 — agrees with the lattice L q of subspaces of Hilbert space. It has been shown that these lattices are in fact isomorphic. (shrink)

Weak measurements offer new insights into the behavior of quantum systems. Combined with post-selection, quantum mechanics predicts a range of new experimentally testable phenomena. In this paper I consider weak measurements performed on time-dependent pre- and post-selected ensembles, with emphasis on the decay of excited states. The results show that the standard exponential decay law is a limiting case of a more general law that depends on both the time of post-selection and the choice of final state. The (...) generalized law is illustrated for two interesting choices of post-selection. (shrink)

Eastern philosophy and western science have convergent and divergent viewpoints for their explanation of consciousness. Convergence is found for the practice of meditation allowing besides a time dependent consciousness, the experience of a timeless consciousness and its beneficial effect on psychological wellbeing and medical improvements, which are confirmed by multiple scientific publications. Theories of quantum mechanics with non-locality and timelessness also show astonishing correlation to eastern philosophy, such as the theory of Penrose-Hameroff (ORC-OR), which explains consciousness by reduction of (...) quantum superposition in the brain. Divergence appears in the interpretation of the subjective experience of timeless consciousness. In eastern philosophy, meditation at a higher level of awareness allows the personal experience of timeless and non-dual consciousness, considered as an empirical proof for the existence of pure consciousness or spirituality existing before the material world and creating it by design. Western science acknowledges the subjective, non-dual experience, and its multiple beneficial effects, however, the interpretation of spirituality designing the material universe is in disagreement with the Darwinian Theory of mutation and selection. A design should create an ideal universe without the injustice of 3% congenital birth defects and later genetic health problems. The western viewpoint of selection is more adapted to explain congenital errors. The gap between subjectivity and objectivity, the mind-body problem, is in eastern philosophy reduced to the dominance of subjectivity over objectivity, whereas western science attributes equal values to both. Nevertheless, there remains an astonishing complementarity between eastern and western practices. (shrink)

Marginal structural models can be used to estimate the causal effect of a potentially time-varying treatment in the presence of time-dependent confounding via weighted regression. The standard approach of using inverse probability of treatment weighting can be sensitive to model misspecification and lead to high-variance estimates due to extreme weights. Various methods have been proposed to partially address this, including covariate balancing propensity score to mitigate treatment model misspecification, and truncation and stabilized-IPTW to temper extreme weights. In this (...) article, we present kernel optimal weighting, a convex-optimization-based approach that finds weights for fitting the MSMs that flexibly balance time-dependent confounders while simultaneously penalizing extreme weights, directly addressing the above limitations. We further extend KOW to control for informative censoring. We evaluate the performance of KOW in a simulation study, comparing it with IPTW, sIPTW, and CBPS. We demonstrate the use of KOW in studying the effect of treatment initiation on time-to-death among people living with human immunodeficiency virus and the effect of negative advertising on elections in the United States. (shrink)

This book offers the first comprehensive introduction to wave scattering in nonstationary materials. G. F. Roach's aim is to provide an accessible, self-contained resource for newcomers to this important field of research that has applications across a broad range of areas, including radar, sonar, diagnostics in engineering and manufacturing, geophysical prospecting, and ultrasonic medicine such as sonograms. New methods in recent years have been developed to assess the structure and properties of materials and surfaces. When light, sound, or some other (...) wave energy is directed at the material in question, "imperfections" in the resulting echo can reveal a tremendous amount of valuable diagnostic information. The mathematics behind such analysis is sophisticated and complex. However, while problems involving stationary materials are quite well understood, there is still much to learn about those in which the material is moving or changes over time. These so-called non-autonomous problems are the subject of this fascinating book. Roach develops practical strategies, techniques, and solutions for mathematicians and applied scientists working in or seeking entry into the field of modern scattering theory and its applications. Wave Scattering by Time-Dependent Perturbations is destined to become a classic in this rapidly evolving area of inquiry. (shrink)

It is shown that the time-dependent WKB expansion highlights some of the hidden properties of the Schrödinger equation and forms a natural bridge between that equation and the functional integral formulation of quantum mechanics. In particular it is shown that the leading (zero- and first-order in ħ) terms in the WKB expansion are essentially classical, and the relationship of this result to the classical nature of the WKB partition function, and of the anomalies in quantum field theory, is discussed.

Starting from the early 2000s, paired associative stimulation protocols have been used in humans to study brain connectivity in motor and sensory networks by exploiting the intrinsic properties of timing-dependent cortical plasticity. In the last 10 years, PAS have also been developed to investigate the plastic properties of complex cerebral systems, such as the frontal ones, with promising results. In the present work, we review the most recent advances of this technique, focusing on protocols targeting frontal cortices to investigate connectivity (...) and its plastic properties, subtending high-order cognitive functions like memory, decision-making, attentional, or emotional processing. Overall, current evidence reveals that PAS can be effectively used to assess, enhance or depress physiological connectivity within frontal networks in a timing-dependent way, in turn modulating cognitive processing in healthy and pathological conditions. (shrink)

If the energy-absorbing radio-frequency spin-flipping device used in perfect crystal neutron interferometry is an intermediate measuring device, then the experimental results contradict the associated wave packet collapse and support the real existence of the de Broglie pilot waves in both arms while the neutron travels in only one.

Nikos K. Logothetis University of Manchester, Manchester, UK In binocular rivalry, the visual percept alternates stochastically between two dichoptically presented stimuli. It is established that both processes related to the eye of origin and binocular, stimulus-related processes account for these fluctuations in conscious perception. Here we studied how their relative contributions vary over time. We applied brief disruptions to rivalry displays, concurrent with an optional eye swap, at varying time intervals after one stimulus became visible (dominant). We found (...) that early in a dominance phase the dominant eye determined the percept by stabilizing its own contribution (regardless of the stimulus), with an additional yet weaker stabilizing contribution of the stimulus (regardless of the eye). Their stabilizing contributions declined in parallel with time so that late in a dominance phase the stimulus (and in some cases also the eye-based) contribution turned negative, favoring a perceptual (or ocular) switch. Our findings show that depending on the time, first processes related to the eye of origin and then those related to the stimulus can have a greater net influence on the stability of the conscious percept. Their co-varying change may be due to feedback from image- to eyeof-origin representations. (shrink)

The statistical properties of a single quantum object and an ensemble of independent such objects are considered in detail for two-level systems. Computer simulations of dynamic zero-point quantum fluctuations for a single quantum object are reported and compared with analytic solutions for the ensemble case.

Quantal penetration through a (stationary) one-dimensional potential barrier is considered as a time evolution of an initially prepared wave packet. The large-time asymptotics of the process is concerned. Locality of the potential imposes certain analytical properties of the interaction amplitudes in the energy representation. The results are presented in terms of development of the phase-space (Wigner's) quasi-distribution. The phase-space evolution kernel is constructed, and it is shown that in the presence of a positive potential no part of the (...) distribution is transported faster than the free particle. For the case of a small initial momentum uncertainty, the deformation of the coordinate density is considered, including a possible advance of its maximum, which would not mean any noncausal signal transport. (shrink)

For time-independent fields the Aharonov-Bohm effect has been obtained by idealizing the coordinate space as multiply-connected and using representations of its fundamental homotopy group to provide information on what is physically identified as the magnetic flux. With a time-dependent field, multiple-connectedness introduces the same degree of ambiguity; by taking into account electromagnetic fields induced by the time dependence, full physical behavior is again recovered once a representation is selected. The selection depends on a single arbitrary (...) class='Hi'>time (hence the so-called holonomies are not unique), although no physical effects depend on the value of that particular time. These features can also be phrased in terms of the selection of self-adjoint extensions, thereby involving yet another question that has come up in this context, namely, boundary conditions for the wave function. (shrink)

Analysing time-dependent independent variables requires the use of process-oriented statistical models. Yet social scientists have often had to use data collected at a single point in time, making their task difficult. Making several assumptions about the covariates, the present study uses survival analysis and other statistical techniques to analyse the 1996 South African population census data and examine the effects of selected independent variables on the timing of parenthood in the country. It was found that the onset of (...) parenthood occurs late in South Africa compared with the pattern in most other African societies. While education plays a role in the postponement of parenthood within racial groups, it fails to explain the differences between African and Coloured women on the one hand, and White and Asian women on the other hand, a finding that suggests the existence of two regimes of family formation in South African society. (shrink)

The two center time dependent Dirac equation, for an electron in the external field of two colliding ultrarelativistic heavy ions is considered. In the ultrarelativistic limit, the ions are practically moving at the speed of light and the electromagnetic fields of the ions are confined to the light fronts by the extreme Lorentz contraction and by the choice of gauge, designed to remove the long-range Coulomb effects. An exact solution to the ultrarelativistic limit of the two-center Dirac equation is (...) found by using light-front variables and a light-fronts representation. Previously unexplained experimental results obtained at CERN's SPS are explained in this way and predictions are made as to where one should look, in momentum space, and in space-time, if one wants to study and observe non-perturbative electromagnetic pair-production effects in extremely relativistic heavy-ion collisions. (shrink)

Knearest neighbor search is an important problem in location-based services and has been well studied on static road networks. However, in real world, road networks are often time-dependent; i.e., the time for traveling through a road always changes over time. Most existing methods forkNN query build various indexes maintaining the shortest distances for some pairs of vertices on static road networks. Unfortunately, these methods cannot be used for the time-dependent road networks because the shortest distances always (...) change over time. To address the problem ofkNN query on time-dependent road networks, we propose a novel voronoi-based index in this paper. Furthermore, we propose a novel balanced tree, namedV-tree, which is a secondary level index on voronoi-based index to make our querying algorithm more efficient. Moreover, we propose an algorithm for preprocessing time-dependent road networks such that the waiting time is not necessary to be considered. We confirm the efficiency of our method through experiments on real-life datasets. (shrink)

Why and how have supply chain codes of conduct diffused among lead firms around the globe? Prior research has drawn on both institutional and stakeholder theories to explain the adoption of codes, but no study has modeled adoption as a temporally dynamic process of diffusion. We propose that the drivers of adoption shift over time, from exclusively nonmarket to eventually market-based mechanisms as well. In an analysis of an original data set of more than 1,800 firms between the years (...) 2006 and 2015, we find that strong nonmarket labor institutions in a firm’s home country are critical to initiating and sustaining the diffusion process. Market mechanisms, such as investor scrutiny and brand risk, emerge as important later. Contrary to prior research, we did not find a significant effect from nongovernmental organization (NGO) pressure. We conclude that markets for corporate social responsibility can and do arise, but only after they are effectuated by nonmarket institutions. (shrink)

Using linear invariant operators in a constructive way we find the most general thermal density operator and Wigner function for time-dependent generalized oscillators. The general Wigner function has five free parameters and describes the thermal Wigner function about a classical trajectory in phase space. The contour of the Wigner function depicts an elliptical orbit with a constant area moving about the classical trajectory, whose eccentricity determines the squeezing of the initial vacuum.

This book provides a novel framework for understanding and revising labor markets and education policies in an era of machine learning. It posits that while learning and knowing both require thinking, learning is fundamentally different than knowing because it results in cognitive processes that change over time. Learning, in contrast to knowing, requires time and agency. Therefore, “learning algorithms”—that enable machines to modify their actions based on real-world experiences—are a fundamentally new form of artificial intelligence that have potential (...) to be even more disruptive to labor markets than prior introductions of digital technology. To explore the difference between knowing and learning, Turing’s “Imitation Game,”—that he proposed as a test for machine thinking—is expanded to include time dependence. The arguments presented in the book introduce three novel concepts: (1) Comparative learning advantage: This is a concept analogous to comparative labor advantage but arises from the disparate times required to learn new knowledge bases/skillsets. It is argued that in the future, comparative learning advantages between humans and machines will determine their division of labor. (2) Two dimensions of job performance—expertise and interpersonal: Job tasks can be sorted into two broad categories. Tasks that require expertise have stable endpoints, which makes these tasks inherently repetitive and subject to automation. Tasks that are interpersonal are highly context-dependent and lack stable endpoints, which makes these tasks inherently non-routine. Humans compared to machines have a comparative learning advantage along the interpersonal dimension, which is increasing in value economically. (3) The Learning Game is a time-dependent version of Turing’s “Imitation Game.” It is more than a thought experiment. The “Learning Game” provides a mathematical framework with quantitative criteria for training and assessing comparative learning advantages. The book is highly interdisciplinary—presenting philosophical arguments in economics, artificial intelligence, and education. It also provides data, mathematical analysis, and testable criteria that researchers in these fields will find of practical use. The book calls for a rethinking of how labor markets operate and how the education system should prepare students for future jobs. It concludes with a list of counterintuitive recommendations for future education and labor policies that all stakeholders—employers, employees, educators, students, and political leaders—should heed. (shrink)

Few have done more than Martin Gutzwiller to clarify the connection between classical time-dependent motion and the time-independent states of quantum systems. Hence it seems appropriate to include the following discussion of the origins of the time-dependent Schrödinger equation in this volume dedicated to him.

A model for kinetics of circular substrate cleavage by restriction endonuclease was formulated. The aim of the analysis of the model was to extract kinetic constants for all target sites from time- dependence of fragment concentration in reaction products. That was proved to be possible for molecules with an odd number of fragments only. A symmetry of the molecules with an even number of fragment is the cause. A solution for molecules with an odd number of fragments was (...) found and methods for dealing with the other molecules were suggested. (shrink)