Determinantal measures related to big q-Jacobi polynomials

We define a novel combinatorial object—the extended Gelfand—Tsetlin graph with cotransition probabilities depending on a parameter q. The boundary of this graph admits an explicit description. We introduce a family of probability measures on the boundary and describe their correlation functions. These measures are a q-analogue of the spectral measures studied earlier in the context of the problem of harmonic analysis on the infinite-dimensional unitary group

Monomial integrals on the classical groups

This paper presents a powerfull method to integrate general monomials on the classical groups with respect to their invariant (Haar) measure. The method has first been applied to the orthogonal group in [J. Math. Phys. 43, 3342 (2002)], and is here used to obtain similar integration formulas for the unitary and the unitary symplectic group. The integration formulas turn out to be of similar form. They are all recursive, where the recursion parameter is the number of column (row) vectors from which the elements in the monomial are taken. This is an important difference to other integration methods. The integration formulas are easily implemented in a computer algebra environment, which allows to obtain analytical expressions very efficiently. Those expressions contain the matrix dimension as a free parameter.Comment: 16 page

Simulation of static and random errors on Grover's search algorithm implemented in a Ising nuclear spin chain quantum computer with few qubits

We consider Grover's search algorithm on a model quantum computer implemented on a chain of four or five nuclear spins with first and second neighbour Ising interactions. Noise is introduced into the system in terms of random fluctuations of the external fields. By averaging over many repetitions of the algorithm, the output state becomes effectively a mixed state. We study its overlap with the nominal output state of the algorithm, which is called fidelity. We find either an exponential or a Gaussian decay for the fidelity as a function of the strength of the noise, depending on the type of noise (static or random) and whether error supression is applied (the 2pi k-method) or not.Comment: 18 pages, 8 figures, extensive revision with new figure

Occurrence of photosynthetic microbial mats in a Lower Cretaceous black shale (central Italy): a shallow-water deposit

Cretaceous oceanic anoxic events (OAEs) were periods of high organic carbon burial corresponding to intervals with excellent organic matter (OM) preservation. This work focuses on the Urbino level, i.e., OAE1b, which is thought to be of regional extent. A detailed microscopical study of OM shows a dominance of microbial activity, characterized by a typical arrangement of exopolymeric substances (EPS) related to microbial mats, bacterial bodies, and some photosynthetic microorganisms, as shown by thylakoids. The latter lived where they have been found, i.e., at the sea bottom, which indicates that OM results from the diagenesis of benthic photosynthetic microbial mats, an interpretation supported through the comparison with a recent analogue. The exceptional preservation of such organic structures in OM points to the joint role of the selective and sorptive preservation pathways. These data and interpretation strongly differ from previous observations in OAE1b equivalents. They suggest that the Urbino level might be an atypical OAE of regional/local extent which was formed within the photic zon

A random matrix approach to decoherence

In order to analyze the effect of chaos or order on the rate of decoherence in a subsystem, we aim to distinguish effects of the two types of dynamics by choosing initial states as random product states from two factor spaces representing two subsystems. We introduce a random matrix model that permits to vary the coupling strength between the subsystems. The case of strong coupling is analyzed in detail, and we find no significant differences except for very low-dimensional spaces.Comment: 11 pages, 5 eps-figure

Transhistoricism and a New Regime of Temporality in Modern Historical Culture

The author associates the return of interest in the historical past and conflicts over its interpretation with significant changes in the historical culture and in the regime of historical temporality. Public representations of history in the context of modern transformations appeal mainly not to reason and authenticity, but to imagination, affects, entertainment and a sense of belonging. These changes are associated with globalization, digitalization and the reorientation of modern society from production to consumption. In historical culture, the consequences of these transformations are plurality, virtualization and presentism. This provokes a blurring of the sense of historical duration and images of the future. The images of the past obey the retroactive logic of extrapolation of current ideas. The appeal to historical grand-narratives in these conditions does not allow, as it was before, to achieve social integration, but on the contrary, provokes conflicts. The new wars of memory are characterized by the hybrid historicism, which is seen as a product of the transformation of fragments of the old grand narratives that now function in a fundamentally changed society. Along with the signs indicating the crisis of the previous model of representation of history, new tendencies are observed. They are manifested, in particular, in the reassembly of history in the multiple perspectives of transhistoricism, a revolutionary view of history unlike the traditional one, the approach which contributes to the coexistence of antinomianism and conformism, the acceptance of differences and the establishment of the boundaries of one’s own identity, playfulness and the desire for authenticity. Thus, transhistorism serves as a vehicle to promote coexistence of multiple stories that work together and through their interconnectedness help to overcome contradictions that once were deemed impossible to handle and to add to a shared sense of unity. The new regime of temporality is considered in the context of removing the contradiction between the progressive spirit of modernism and the deconstruction of historicism in the postmodern idea of post-history. The temporality of transhistoricism is determined by the nonlinearity of the time of culture, in which complex interactions of the constructed, deconstructed and reconstructed, lost, acquired and restored take place

Ancient Understanding of Time and the Background of Contemporary Historicism

Contemporary changes in historical culture associated with various states of modernity actualize the problem of the foundations and prerequisites of historicism as a principle of thinking characteristic of modern societies. The ancient historicism background consists primarily in the advanced concepts of time and eternity, which contain the potential variability in the understanding of historicity in modern philosophy and culture. At the same time, the problem of the historical variability of the world remained on the periphery of ancient philosophy and culture, and classical historicism, which was established in the second half of the 18th century, was based on the rejection of some aspects of the ancient heritage. In opposing being and becoming, ancient philosophy preferred being, which was also manifested in the preference for truth over time, for one over multiple. Classical historicism of modern times is focused on the idea of becoming, which in a new way reveals the contradictions between truth and time, one and multiple. Relativism and plurality are becoming features of modern transformations of historicism, in which the structures of time are preserved, dating back to the ancient concepts of chronos, kairos, eon, etc. Of particular interest are modern ideas about time, which go back to the ancient concept of objectified chronological time and its correlation with other forms of time conceptualization. In the historical consciousness of modern times, the ancient concepts of time were transformed under the influence of the prophetic sense of time, characteristic of the biblical tradition, in which the historical process is considered in the context of the gradual revelation of the original intention and meaning of history

Dysflective cones: Visual function and cone reflectivity in long-term follow-up of acute bilateral foveolitis.

PURPOSE:Confocal adaptive optics scanning laser ophthalmoscope (AOSLO) images provide a sensitive measure of cone structure. However, the relationship between structural findings of diminished cone reflectivity and visual function is unclear. We used fundus-referenced testing to evaluate visual function in regions of apparent cone loss identified using confocal AOSLO images. METHODS:A patient diagnosed with acute bilateral foveolitis had spectral-domain optical coherence tomography (SD-OCT) (Spectralis HRA + OCT system [Heidelberg Engineering, Vista, CA, USA]) images indicating focal loss of the inner segment-outer segment junction band with an intact, but hyper-reflective, external limiting membrane. Five years after symptom onset, visual acuity had improved from 20/80 to 20/25, but the retinal appearance remained unchanged compared to 3 months after symptoms began. We performed structural assessments using SD-OCT, directional OCT (non-standard use of a prototype on loan from Carl Zeiss Meditec) and AOSLO (custom-built system). We also administered fundus-referenced functional tests in the region of apparent cone loss, including analysis of preferred retinal locus (PRL), AOSLO acuity, and microperimetry with tracking SLO (TSLO) (prototype system). To determine AOSLO-corrected visual acuity, the scanning laser was modulated with a tumbling E consistent with 20/30 visual acuity. Visual sensitivity was assessed in and around the lesion using TSLO microperimetry. Complete eye examination, including standard measures of best-corrected visual acuity, visual field tests, color fundus photos, and fundus auto-fluorescence were also performed. RESULTS:Despite a lack of visible cone profiles in the foveal lesion, fundus-referenced vision testing demonstrated visual function within the lesion consistent with cone function. The PRL was within the lesion of apparent cone loss at the fovea. AOSLO visual acuity tests were abnormal, but measurable: for trials in which the stimulus remained completely within the lesion, the subject got 48% correct, compared to 78% correct when the stimulus was outside the lesion. TSLO microperimetry revealed reduced, but detectible, sensitivity thresholds within the lesion. CONCLUSIONS AND IMPORTANCE:Fundus-referenced visual testing proved useful to identify functional cones despite apparent photoreceptor loss identified using AOSLO and SD-OCT. While AOSLO and SD-OCT appear to be sensitive for the detection of abnormal or absent photoreceptors, changes in photoreceptors that are identified with these imaging tools do not correlate completely with visual function in every patient. Fundus-referenced vision testing is a useful tool to indicate the presence of cones that may be amenable to recovery or response to experimental therapies despite not being visible on confocal AOSLO or SD-OCT images