Algebras of Measurements: the logical structure of Quantum Mechanics

In Quantum Physics, a measurement is represented by a projection on some closed subspace of a Hilbert space. We study algebras of operators that abstract from the algebra of projections on closed subspaces of a Hilbert space. The properties of such operators are justified on epistemological grounds. Commutation of measurements is a central topic of interest. Classical logical systems may be viewed as measurement algebras in which all measurements commute. Keywords: Quantum measurements, Measurement algebras, Quantum Logic. PACS: 02.10.-v.Comment: Submitted, 30 page

Partial order and a T0T_0-topology in a set of finite quantum systems

A `whole-part' theory is developed for a set of finite quantum systems $\Sigma (n)$ with variables in ${\mathbb Z}(n)$. The partial order `subsystem' is defined, by embedding various attributes of the system $\Sigma (m)$ (quantum states, density matrices, etc) into their counterparts in the supersystem $\Sigma (n)$ (for $m|n$). The compatibility of these embeddings is studied. The concept of ubiquity is introduced for quantities which fit with this structure. It is shown that various entropic quantities are ubiquitous. The sets of various quantities become $T_0$-topological spaces with the divisor topology, which encapsulates fundamental physical properties. These sets can be converted into directed-complete partial orders (dcpo), by adding `top elements'. The continuity of various maps among these sets is studied

Continuous slice functional calculus in quaternionic Hilbert spaces

The aim of this work is to define a continuous functional calculus in quaternionic Hilbert spaces, starting from basic issues regarding the notion of spherical spectrum of a normal operator. As properties of the spherical spectrum suggest, the class of continuous functions to consider in this setting is the one of slice quaternionic functions. Slice functions generalize the concept of slice regular function, which comprises power series with quaternionic coefficients on one side and that can be seen as an effective generalization to quaternions of holomorphic functions of one complex variable. The notion of slice function allows to introduce suitable classes of real, complex and quaternionic $C^*$--algebras and to define, on each of these $C^*$--algebras, a functional calculus for quaternionic normal operators. In particular, we establish several versions of the spectral map theorem. Some of the results are proved also for unbounded operators. However, the mentioned continuous functional calculi are defined only for bounded normal operators. Some comments on the physical significance of our work are included.Comment: 71 pages, some references added. Accepted for publication in Reviews in Mathematical Physic

Syntax-like structures in maternal contact calls of Chestnut-Crowned Babblers (Pomatostomus ruficeps)

The combination of meaning-bearing units (e.g., words) into higher-order structures (e.g., compound words and phrases) is integral to human language. Despite this central role of syntax in language, little is known about its evolutionary progression. Comparative data using animal communication systems offer potential insights, but only a handful of species have been identified to combine meaningful calls together into larger signals. We investigated a candidate for syntax-like structure in the highly social chestnut-crowned babbler (Pomatostomus ruficeps). Using a combination of behavioral observations, acoustic analyses, and playback experiments, we test whether the form and function of maternal contact calls is modified by combining the core “piping” elements of such calls with at least one other call element or call. Results from the acoustic analyses (236 analysed calls from 10 individuals) suggested that piping call elements can be flexibly initiated with either “peow” elements from middle-distance contact calls or adult “begging” calls to form “peow-pipe” and “beg-pipe” calls. Behavioral responses to playbacks (20 trials to 7 groups) of natural peow-pipe and beg-pipe calls were comparable to those of artificially generated versions of each call using peow elements and begging calls from other contexts. Furthermore, responses to playbacks (34 trials to 7 groups) of the three forms of maternal contact calls (piping alone, peow-pipe, beg-pipe) differed. Together these data suggest that meaning encoded in piping calls is modified by combining such calls with begging calls or peow elements used in other contexts and so provide rare empirical evidence for syntactic-like structuring in a nonhuman animal

Combinatoriality in the vocal systems of nonhuman animals

A key challenge in the field of human language evolution is the identification of the selective conditions that gave rise to language's generative nature. Comparative data on nonhuman animals provides a powerful tool to investigate similarities and differences among nonhuman and human communication systems and to reveal convergent evolutionary mechanisms. In this article, we provide an overview of the current evidence for combinatorial structures found in the vocal system of diverse species. We show that considerable structural diversity exits across and within species in the forms of combinatorial structures used. Based on this we suggest that a fine‐grained classification and differentiation of combinatoriality is a useful approach permitting systematic comparisons across animals. Specifically, this will help to identify factors that might promote the emergence of combinatoriality and, crucially, whether differences in combinatorial mechanisms might be driven by variations in social and ecological conditions or cognitive capacities

A new Late Agenian (MN2a, Early Miocene) fossil assemblage from Wallenried (Molasse Basin, Canton Fribourg, Switzerland)

Excavations of two fossiliferous layers in the Wallenried sand- and marl pit produced a very diversified vertebrate fauna. New material allows the reassessment of the taxonomic position of the ruminant taxa Andegameryx andegaviensis and endemic Friburgomeryx wallenriedensis. An emended diagnosis for the second species is provided and additional material of large and small mammals, as well as ectothermic vertebrates, is described. The recorded Lagomorpha show interesting morphological deviations from other Central European material, and probably represent a unique transitional assemblage with a co-occurrence of Titanomys, Lagopsis and Prolagus. Rodentia and Eulipotyphla belong to typical and well-known species of the Agenian of the Swiss Molasse Basin. Abundant small mammal teeth have allowed us to pinpoint the biostratigraphic age of Wallenried to late MN2a. The biostratigraphic age conforms to data derived from the charophyte assemblages and confirms the oldest occurrence of venomous snake fangs. The palaeoenvironmental context is quite complex. Sedimentary structures and fauna (fishes, frogs, salamanders, ostracods) are characteristic for a humid, lacustrine environment within a flood plain system

Phytochrome-Based Extracellular Matrix with Reversibly Tunable mechanical Properties

Interrogation and control of cellular fate and function using optogenetics is providing revolutionary insights into biology. Optogenetic control of cells is achieved by coupling genetically encoded photoreceptors to cellular effectors and enables unprecedented spatiotemporal control of signaling processes. Here, a fast and reversibly switchable photoreceptor is used to tune the mechanical properties of polymer materials in a fully reversible, wavelength‐specific, and dose‐ and space‐controlled manner. By integrating engineered cyanobacterial phytochrome 1 into a poly(ethylene glycol) matrix, hydrogel materials responsive to light in the cell‐compatible red/far‐red spectrum are synthesized. These materials are applied to study in human mesenchymal stem cells how different mechanosignaling pathways respond to changing mechanical environments and to control the migration of primary immune cells in 3D. This optogenetics‐inspired matrix allows fundamental questions of how cells react to dynamic mechanical environments to be addressed. Further, remote control of such matrices can create new opportunities for tissue engineering or provide a basis for optically stimulated drug depots

Lower and upper probabilities in the distributive lattice of subsystems

yesThe set of subsystems ∑ (m) of a finite quantum system ∑(n) (with variables in Ζ(n)) together with logical connectives, is a distributive lattice. With regard to this lattice, the ℓ(m | ρn) = Tr ((m) ρn ) (where (m) is the projector to ∑(m)) obeys a supermodularity inequality, and it is interpreted as a lower probability in the sense of the Dempster–Shafer theory, and not as a Kolmogorov probability. It is shown that the basic concepts of the Dempster–Shafer theory (lower and upper probabilities and the Dempster multivaluedness) are pertinent to the quantum formalism of finite systems