On Nonzero Kronecker Coefficients and their Consequences for Spectra

A triple of spectra (r^A, r^B, r^{AB}) is said to be admissible if there is a density operator rho^{AB} with (Spec rho^A, Spec rho^B, Spec rho^{AB})=(r^A, r^B, r^{AB}). How can we characterise such triples? It turns out that the admissible spectral triples correspond to Young diagrams (mu, nu, lambda) with nonzero Kronecker coefficient [M. Christandl and G. Mitchison, to appear in Comm. Math. Phys., quant-ph/0409016; A. Klyachko, quant-ph/0409113]. This means that the irreducible representation V_lambda is contained in the tensor product of V_mu and V_nu. Here, we show that such triples form a finitely generated semigroup, thereby resolving a conjecture of Klyachko. As a consequence we are able to obtain stronger results than in [M. Ch. and G. M. op. cit.] and give a complete information-theoretic proof of the correspondence between triples of spectra and representations. Finally, we show that spectral triples form a convex polytope.Comment: 13 page

Close range photogrammetry in the survey of the coastal area geoecological conditions (on the example of Portugal)

Close range digital photogrammetry, which involves the application of unmanned aerial vehicle (UAV), has been used in a growing number of diverse applications across different scientific disciplines. Our objective was to use the mentioned method in the survey of the contemporary geoecological conditions of the coastal area on the example of Portuguese northwest coastal zone. The coastal zone can be subdivided into two geomorphological sectors: Sector 1, between the Minho River and the town of Espinho, where the coastal segments consist of estuaries, sandy and shingle beaches with rocky outcrops, and Holocene dune systems. The estuaries and the foredunes in particular are very degraded by human activities; and Sector 2, between Espinho and the Mondego Cape, where coastal lagoons and Holocene dune systems occur. We chose two beaches for surveying – Aguçadoura and Ramalha to which the drone swinglet CAM took the photos. We used the ground control software eMotion 2 to plan the flights over the study area and controlled the drone’s trajectory during flight. After processing the obtained images in the program of AgisoftPhotoscanPro, we generated the 2D orthophotos and 3D digital elevation models (DEM) of the research sections. At this stage of study we derived the above product without using the ground control points, or we used only the camera GPS data. Based on these models the compilation of the large-scale maps of high resolution (1cm-5cm) will be possible in the GISs for monitoring and management of the geoecological state of the mentioned beaches in case to precise the x, y and z values of the models with the geodetic device of Differential GPSs in the selected ground control points (GCP).We are grateful to the European Commission ERASMUS-MUNDUS Action-2 ELECTRA program and the Earth Sciences Centre of the University of Minho (Braga, Portugal) in supporting us to conduct the field works and research.info:eu-repo/semantics/publishedVersio

The Principal Element of a Frobenius Lie Algebra

We introduce the notion of the \textit{principal element} of a Frobenius Lie algebra \f. The principal element corresponds to a choice of F\in \f^* such that $F[-,-]$ non-degenerate. In many natural instances, the principal element is shown to be semisimple, and when associated to \sl_n, its eigenvalues are integers and are independent of $F$. For certain ``small'' functionals $F$, a simple construction is given which readily yields the principal element. When applied to the first maximal parabolic subalgebra of \sl_n, the principal element coincides with semisimple element of the principal three-dimensional subalgebra. We also show that Frobenius algebras are stable under deformation.Comment: 10 page

Relict basin closure and crustal shortening budgets during continental collision: An example from Caucasus sediment provenance

Comparison of plate convergence with the timing and magnitude of upper crustal shortening in collisional orogens indicates both shortening deficits (200–1700 km) and significant (10–40%) plate deceleration during collision, the cause(s) for which remains debated. The Greater Caucasus Mountains, which result from postcollisional Cenozoic closure of a relict Mesozoic back‐arc basin on the northern margin of the Arabia‐Eurasia collision zone, help reconcile these debates. Here we use U‐Pb detrital zircon provenance data and the regional geology of the Caucasus to investigate the width of the now‐consumed Mesozoic back‐arc basin and its closure history. The provenance data record distinct southern and northern provenance domains that persisted until at least the Miocene. Maximum basin width was likely ~350–400 km. We propose that closure of the back‐arc basin initiated at ~35 Ma, coincident with initial (soft) Arabia‐Eurasia collision along the Bitlis‐Zagros suture, eventually leading to ~5 Ma (hard) collision between the Lesser Caucasus arc and the Scythian platform to form the Greater Caucasus Mountains. Final basin closure triggered deceleration of plate convergence and tectonic reorganization throughout the collision. Postcollisional subduction of such small (102–103 km wide) relict ocean basins can account for both shortening deficits and delays in plate deceleration by accommodating convergence via subduction/underthrusting, although such shortening is easily missed if it occurs along structures hidden within flysch/slate belts. Relict basin closure is likely typical in continental collisions in which the colliding margins are either irregularly shaped or rimmed by extensive back‐arc basins and fringing arcs, such as those in the modern South Pacific.Key PointsU‐Pb provenance indicates Greater Caucasus formed by postcollisional Cenozoic closure of a Mesozoic back arc basin likely ~350–400 km widePostcollisional subduction/underthrusting of such relict basins helps account for shortening deficits and delayed plate decelerationPlate convergence should not be expected to balance upper crustal shortening or the length of subducted slab following collisionPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135981/1/tect20504.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/135981/2/tect20504_am.pd

Moduli in Exceptional SUSY Gauge Theories

The low energy structures of N=1 supersymmetric models with E_6, F_4 and E_7 gauge groups and fundamental irrep matter contents are studied herein. We identify sets of gauge invariant composites which label all flat directions in the confining/Higgs phases of these theories. The impossibility of mapping several of these primary operators rules out previously conjectured exceptional self duals reported in the literature.Comment: 20 pages, harvmac and tables macro

Dual Descriptions of SO(10) SUSY Gauge Theories with Arbitrary Numbers of Spinors and Vectors

We examine the low energy structure of N=1 supersymmetric SO(10) gauge theory with matter chiral superfields in N_Q spinor and N_f vector representations. We construct a dual to this model based upon an SU(N_f+2N_Q-7) x Sp(2N_Q-2) gauge group without utilizing deconfinement methods. This product theory generalizes all previously known Pouliot-type duals to SO(N_c) models with spinor and vector matter. It also yields large numbers of new dual pairs along various flat directions. The dual description of the SO(10) theory satisfies multiple consistency checks including an intricate renormalization group flow analysis which links it with Seiberg's duality transformations. We discuss its implications for building grand unified theories that contain all Standard Model fields as composite degrees of freedom.Comment: 36 pages, harvmac and tables macros, 1 figur

Human-environmental interactions and seismic activity in a Late Bronze to Early Iron Age settlement center in the southeastern Caucasus

Long-term human-environmental interactions in naturally fragile drylands are a focus of geomorphological and geoarchaeological research. Furthermore, many dryland societies were also affected by seismic activity. The semi-arid Shiraki Plain in the tectonically active southeastern Caucasus is currently covered by steppe and largely devoid of settlements. However, numerous Late Bronze to Early Iron Age city-type settlements suggest early state formation between ca. 3.2-2.5 ka that abruptly ended after that time. A paleolake was postulated for the lowest plain, and nearby pollen records suggest forest clearcutting of the upper altitudes under a more humid climate during the Late Bronze/Early Iron Ages. Furthermore, also an impact of earthquakes on regional Early Iron Age settlements was suggested. However, regional paleoenvironmental changes and paleoseismicity were not systematically studied so far. We combined geomorphological, sedimentological, chronological and paleoecological data with hydrological modelling to reconstruct regional Holocene paleoenvironmental changes, to identify natural and human causes and to study possible seismic events during the Late Bronze/Early Iron Ages. Our results show a balanced to negative Early to Mid-Holocene water balance probably caused by forested upper slopes. Hence, no lake but a pellic Vertisol developed in the lowest plain. Following, Late Bronze/Early Iron Age forest clear-cutting caused lake formation and the deposition of lacustrine sediments derived from soil erosion. Subsequently, regional aridification caused slow lake desiccation. Remains of freshwater fishes indicate that the lake potentially offered valuable ecosystem services for regional prehistoric societies even during the desiccation period. Finally, colluvial coverage of the lake sediments during the last centuries could have been linked with hydrological extremes during the Little Ice Age. Our study demonstrates that the Holocene hydrological balance of the Shiraki Plain was and is situated near a major hydrological threshold, making the landscape very sensitive to small-scale human or natural influences with severe consequences for local societies. Furthermore, seismites in the studied sediments do not indicate an influence of earthquakes on the main and late phases of Late Bronze/Early Iron Age settlement. Altogether, our study underlines the high value of multi-disciplinary approaches to investigate human-environmental interactions and paleoseismicity in drylands on millennial to centennial time scales