scholarly journals Can a quantum state over time resemble a quantum state at a single time?

2017 ◽  
Vol 473 (2205) ◽  
pp. 20170395 ◽  
Author(s):  
Dominic Horsman ◽  
Chris Heunen ◽  
Matthew F. Pusey ◽  
Jonathan Barrett ◽  
Robert W. Spekkens
Keyword(s):  
Tensor Product ◽  
Quantum State ◽  
Hilbert Spaces ◽  
Composite System ◽  
Hermitian Operator ◽  
Multiple Time ◽  
Single Time ◽  
Space And Time ◽  
Over Time ◽  
Joint State

The standard formalism of quantum theory treats space and time in fundamentally different ways. In particular, a composite system at a given time is represented by a joint state, but the formalism does not prescribe a joint state for a composite of systems at different times. If there were a way of defining such a joint state, this would potentially permit a more even-handed treatment of space and time, and would strengthen the existing analogy between quantum states and classical probability distributions. Under the assumption that the joint state over time is an operator on the tensor product of single-time Hilbert spaces, we analyse various proposals for such a joint state, including one due to Leifer and Spekkens, one due to Fitzsimons, Jones and Vedral, and another based on discrete Wigner functions. Finding various problems with each, we identify five criteria for a quantum joint state over time to satisfy if it is to play a role similar to the standard joint state for a composite system: that it is a Hermitian operator on the tensor product of the single-time Hilbert spaces; that it represents probabilistic mixing appropriately; that it has the appropriate classical limit; that it has the appropriate single-time marginals; that composing over multiple time steps is associative. We show that no construction satisfies all these requirements. If Hermiticity is dropped, then there is an essentially unique construction that satisfies the remaining four criteria.

scholarly journals Climate and plant community diversity in space and time

2020 ◽  
Vol 117 (9) ◽  
pp. 4464-4470 ◽  
Author(s):  
Susan Harrison ◽  
Marko J. Spasojevic ◽  
Daijiang Li
Keyword(s):  
Plant Community ◽  
Plant Diversity ◽  
Phylogenetic Diversity ◽  
Spatial Scales ◽  
Community Diversity ◽  
Niche Conservatism ◽  
Space And Time ◽  
Drying Trend ◽  
Functional And Phylogenetic Diversity ◽  
Over Time

Climate strongly shapes plant diversity over large spatial scales, with relatively warm and wet (benign, productive) regions supporting greater numbers of species. Unresolved aspects of this relationship include what causes it, whether it permeates to community diversity at smaller spatial scales, whether it is accompanied by patterns in functional and phylogenetic diversity as some hypotheses predict, and whether it is paralleled by climate-driven changes in diversity over time. Here, studies of Californian plants are reviewed and new analyses are conducted to synthesize climate–diversity relationships in space and time. Across spatial scales and organizational levels, plant diversity is maximized in more productive (wetter) climates, and these consistent spatial relationships are mirrored in losses of taxonomic, functional, and phylogenetic diversity over time during a recent climatic drying trend. These results support the tolerance and climatic niche conservatism hypotheses for climate–diversity relationships, and suggest there is some predictability to future changes in diversity in water-limited climates.

scholarly journals Evolution of anatomical concept usage over time: Mining 200 years of biodiversity literature

2017 ◽  
Author(s):  
Prashanti Manda ◽  
Todd J Vision
Keyword(s):  
Scientific Literature ◽  
Concept Drift ◽  
Multiple Time ◽  
Temporal Data Mining ◽  
Temporal Data ◽  
Initial State ◽  
Time Periods ◽  
Historic Record ◽  
Concept Usage ◽  
Over Time

The scientific literature contains an historic record of the changing ways in which we describe the world. Shifts in understanding of scientific concepts are reflected in the introduction of new terms and the changing usage and context of existing ones. We conducted an ontology-based temporal data mining analysis of biodiversity literature from the 1700s to 2000s to quantitatively measure how the context of usage for vertebrate anatomical concepts has changed over time. The corpus of literature was divided into nine non-overlapping time periods with comparable amounts of data and context vectors of anatomical concepts were compared to measure the magnitude of concept drift both between adjacent time periods and cumulatively relative to the initial state. Surprisingly, we found that while anatomical concept drift between adjacent time periods was substantial (55% to 68%), it was of the same magnitude as cumulative concept drift across multiple time periods. Such a process, bound by an overall mean drift, fits the expectations of a mean-reverting process.

Extension of normal functionals on W*-tensor products

1975 ◽  
Vol 78 (2) ◽  
pp. 301-307 ◽  
Author(s):  
Simon Wassermann
Keyword(s):  
Representation Theory ◽  
Tensor Product ◽  
Hilbert Spaces ◽  
General Result ◽  
Von Neumann Algebras ◽  
Tensor Products ◽  
Von Neumann ◽  
Hilbert Algebras ◽  
Special Cases

A deep result in the theory of W*-tensor products, the Commutation theorem, states that if M and N are W*-algebras faithfully represented as von Neumann algebras on the Hilbert spaces H and K, respectively, then the commutant in L(H ⊗ K) of the W*-tensor product of M and N coincides with the W*-tensor product of M′ and N′. Although special cases of this theorem were established successively by Misonou (2) and Sakai (3), the validity of the general result remained conjectural until the advent of the Tomita-Takesaki theory of Modular Hilbert algebras (6). As formulated, the Commutation theorem is a spatial result; that is, the W*-algebras in its statement are taken to act on specific Hilbert spaces. Not surprisingly, therefore, known proofs rely heavily on techniques of representation theory.

scholarly journals An Evaluation of the Implementation of a UK School-Based Running Program

Children ◽  
2020 ◽  
Vol 7 (10) ◽  
pp. 151
Author(s):  
Anna E. Chalkley ◽  
Ash C. Routen ◽  
Jo P. Harris ◽  
Lorraine A. Cale ◽  
Trish Gorely ◽  
...  
Keyword(s):  
Primary Schools ◽  
Average Distance ◽  
Multiple Time ◽  
School Year ◽  
School Based ◽  
Before And After ◽  
The Uk ◽  
High Level ◽  
Academic Year ◽  
Over Time

The adoption of school-based running programs has rapidly increased over the last five years in the UK and globally. However, there is currently a lack of information on how these initiatives are implemented, and whether they are generalizable and/or sustainable. This study evaluated the implementation (including reach, fidelity, and dose) of a school-based running program over seven months to inform future delivery. This observational study used a mixed-method, single-group, before-and-after design strengthened by multiple interim measurements to evaluate the implementation of an optional school-based running program. Five state-funded primary schools in Leicestershire, UK, participated, with 17 teachers and 189 (81 boys (47.4%) and 90 girls (52.6%)) Year 5 pupils (aged 9–10 years) from eight classes. During the 2016/2017 academic year, data were collected via several measures (including interviews, focus groups, observations, questionnaires, and teacher implementation logs) at multiple levels (i.e., school and individual) and at multiple time points during implementation. Follow up qualitative data were also collected during 2017/2018. The school-based running program achieved good reach, with 100% of pupils opting to participate at some point during the academic year. All schools implemented the program with good fidelity, although the level of implementation varied between schools and over time. The average number of sessions held per week ranged from 0.94–3.89 with the average distance accumulated per pupil per week ranging from 0.02 to 2.91 kilometers and boys being more likely than girls to be classed as high-level participators. Despite an initial drop off in participation over time, all schools remained engaged in the program and continued to implement it until the end of the school year. Contextual features (e.g., staff capacity and resources) differed between schools and influenced the quality of implementation and the frequency of delivery. The school-based running program is simple, inexpensive, and versatile and can be implemented by schools with relative ease. However, schools are diverse settings, with unique challenges to ongoing delivery. Thus, planned adaptations, specific to each school’s context, are likely necessary to sustain participation in the longer term and should be considered prior to implementation.

scholarly journals Dynamic changes in cell size and corresponding cell fate after optic nerve injury

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Benjamin M. Davis ◽  
Li Guo ◽  
Nivedita Ravindran ◽  
Ehtesham Shamsher ◽  
Veerle Baekelandt ◽  
...  
Keyword(s):  
Optic Nerve ◽  
Cell Size ◽  
Nerve Injury ◽  
Cell Fate ◽  
Adaptive Optics ◽  
Retinal Cell ◽  
Multiple Time ◽  
Optic Nerve Injury ◽  
Over Time

AbstractIdentifying disease-specific patterns of retinal cell loss in pathological conditions has been highlighted by the emergence of techniques such as Detection of Apoptotic Retinal Cells and Adaptive Optics confocal Scanning Laser Ophthalmoscopy which have enabled single-cell visualisation in vivo. Cell size has previously been used to stratify Retinal Ganglion Cell (RGC) populations in histological samples of optic neuropathies, and early work in this field suggested that larger RGCs are more susceptible to early loss than smaller RGCs. More recently, however, it has been proposed that RGC soma and axon size may be dynamic and change in response to injury. To address this unresolved controversy, we applied recent advances in maximising information extraction from RGC populations in retinal whole mounts to evaluate the changes in RGC size distribution over time, using three well-established rodent models of optic nerve injury. In contrast to previous studies based on sampling approaches, we examined the whole Brn3a-positive RGC population at multiple time points over the natural history of these models. The morphology of over 4 million RGCs was thus assessed to glean novel insights from this dataset. RGC subpopulations were found to both increase and decrease in size over time, supporting the notion that RGC cell size is dynamic in response to injury. However, this study presents compelling evidence that smaller RGCs are lost more rapidly than larger RGCs despite the dynamism. Finally, using a bootstrap approach, the data strongly suggests that disease-associated changes in RGC spatial distribution and morphology could have potential as novel diagnostic indicators.

Aging Couples: Benefits and Costs of Long Intimate Relations

2018 ◽  
Author(s):  
Victoria I. Michalowski ◽  
Denis Gerstorf ◽  
Christiane A. Hoppmann
Keyword(s):  
Time Frame ◽  
Multiple Time Scales ◽  
Future Research ◽  
Multiple Time ◽  
Physical And Mental Health ◽  
Short Term ◽  
Intimate Relations ◽  
Benefits And Costs ◽  
Over Time

Aging does not occur in isolation, but often involves significant others such as spouses. Whether such dyadic associations involve gains or losses depends on a myriad of factors, including the time frame under consideration. What is beneficial in the short term may not be so in the long term, and vice versa. Similarly, what is beneficial for one partner may be costly for the other, or the couple unit over time. Daily dynamics between partners involving emotion processes, health behaviors, and collaborative cognition may accumulate over years to affect the longer-term physical and mental health outcomes of either partner or both partners across adulthood and into old age. Future research should move beyond an individual-focused approach to aging and consider the importance of and interactions among multiple time scales to better understand how, when, and why older spouses shape each other’s aging trajectories, both for better and for worse.

scholarly journals PFASST-ER: combining the parallel full approximation scheme in space and time with parallelization across the method

2020 ◽  
Vol 23 (1-4) ◽  
Author(s):  
Ruth Schöbel ◽  
Robert Speck
Keyword(s):  
High Performance ◽  
Large Scale ◽  
Approximation Scheme ◽  
Reaction Diffusion ◽  
Multiple Time ◽  
Time Step ◽  
Computing Systems ◽  
Space And Time ◽  
Quasi Newton ◽  
Spectral Deferred Correction

AbstractTo extend prevailing scaling limits when solving time-dependent partial differential equations, the parallel full approximation scheme in space and time (PFASST) has been shown to be a promising parallel-in-time integrator. Similar to space–time multigrid, PFASST is able to compute multiple time-steps simultaneously and is therefore in particular suitable for large-scale applications on high performance computing systems. In this work we couple PFASST with a parallel spectral deferred correction (SDC) method, forming an unprecedented doubly time-parallel integrator. While PFASST provides global, large-scale “parallelization across the step”, the inner parallel SDC method allows integrating each individual time-step “parallel across the method” using a diagonalized local Quasi-Newton solver. This new method, which we call “PFASST with Enhanced concuRrency” (PFASST-ER), therefore exposes even more temporal concurrency. For two challenging nonlinear reaction-diffusion problems, we show that PFASST-ER works more efficiently than the classical variants of PFASST and can use more processors than time-steps.

scholarly journals A COMPLETELY ENTANGLED SUBSPACE OF MAXIMAL DIMENSION

2006 ◽  
Vol 04 (02) ◽  
pp. 325-330 ◽  
Author(s):  
B. V. RAJARAMA BHAT
Keyword(s):  
Tensor Product ◽  
Hilbert Spaces ◽  
Product Formula ◽  
Maximal Dimension ◽  
Maximum Dimension ◽  
Dimension Formula ◽  
Finite Dimensional ◽  
Minimum Dimension ◽  
Orthogonal Product ◽  
Product Vector

Consider a tensor product [Formula: see text] of finite-dimensional Hilbert spaces with dimension [Formula: see text], 1 ≤ i ≤ k. Then the maximum dimension possible for a subspace of [Formula: see text] with no non-zero product vector is known to be d1 d2…dk - (d1 + d2 + … + dk + k - 1. We obtain an explicit example of a subspace of this kind. We determine the set of product vectors in its orthogonal complement and show that it has the minimum dimension possible for an unextendible product basis of not necessarily orthogonal product vectors.

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