Duality and ontology

A ‘duality’ is a formal mapping between the spaces of solutions of two empirically equivalent theories. In recent times, dualities have been found to be pervasive in string theory and quantum field theory. Naïvely interpreted, duality-related theories appear to make very different ontological claims about the world—differing in e.g. space-time structure, fundamental ontology, and mereological structure. In light of this, duality-related theories raise questions familiar from discussions of underdetermination in the philosophy of science: in the presence of dual theories, what is one to say about the ontology of the world? In this paper, we undertake a comprehensive and non-technical survey of the landscape of possible ontological interpretations of duality-related theories. We provide a significantly enriched and clarified taxonomy of options—several of which are novel to the literature

Rational invariants of even ternary forms under the orthogonal group

In this article we determine a generating set of rational invariants of minimal cardinality for the action of the orthogonal group $\mathrm{O}_3$ on the space $\mathbb{R}[x,y,z]_{2d}$ of ternary forms of even degree $2d$. The construction relies on two key ingredients: On one hand, the Slice Lemma allows us to reduce the problem to dermining the invariants for the action on a subspace of the finite subgroup $\mathrm{B}_3$ of signed permutations. On the other hand, our construction relies in a fundamental way on specific bases of harmonic polynomials. These bases provide maps with prescribed $\mathrm{B}_3$-equivariance properties. Our explicit construction of these bases should be relevant well beyond the scope of this paper. The expression of the $\mathrm{B}_3$-invariants can then be given in a compact form as the composition of two equivariant maps. Instead of providing (cumbersome) explicit expressions for the $\mathrm{O}_3$-invariants, we provide efficient algorithms for their evaluation and rewriting. We also use the constructed $\mathrm{B}_3$-invariants to determine the $\mathrm{O}_3$-orbit locus and provide an algorithm for the inverse problem of finding an element in $\mathbb{R}[x,y,z]_{2d}$ with prescribed values for its invariants. These are the computational issues relevant in brain imaging.Comment: v3 Changes: Reworked presentation of Neuroimaging application, refinement of Definition 3.1. To appear in "Foundations of Computational Mathematics

Mortar FEs on Overlapping Meshes : Application to Magnetodynamics

Abstract The finite element (FE) method is frequently used in magnetodynamics as well suited to treat problems with complex geometries while keeping a simplicity in the implementation. However, some modelisations, as in eddy current (EC) non destructive testing (NDT), present the particularity to have moving parts. A global remeshing can be necessary which causes expensive CPU time. Domain decomposition methods allowing to take into account the movement without having to remesh the whole computational domain. The mortar element method (MEM), a variational non-conforming domain decomposition approach [1] offers attractive advantages in terms of flexibility and accuracy. In its original version for non-overlapping subdomains, the information is transferred through the skeleton of the decomposition by means of a suitable L 2 -projection of the field trace from the master to the slave subdomains. A MEM with overlapping subdomains has been proposed to coupled a global scalar potential defined everywhere in the considered domain and a local vector potential defined only in (possibly moving) conductor

Price Setting in the Euro Area: Some Stylized Facts from Individual Consumer Price Data.

This paper documents patterns of price setting at the retail level in the euro area. A set of stylized facts on the frequency and size of price changes is presented along with an econometric investigation of their main determinants. Price adjustment in the euro area can be summarized in six stylized facts. First, prices of most products change rarely. The average monthly frequency of price adjustment is 15 p.c., compared to about 25 p.c. in the US. Second, the frequency of price changes is characterized by substantial cross-product heterogeneity and pronounced sectoral patterns: prices of (oil-related) energy and unprocessed food products change very often, while price adjustments are less frequent for processed food products, non-energy industrial goods and services. Third, cross-country heterogeneity exists but is less pronounced. Fourth, price decreases are not uncommon. Fifth, price increases and decreases are sizeable compared to aggregate and sectoral inflation rates. Sixth, price changes are not highly synchronized across price-setters. Moreover, the frequency of price changes in the euro area is related to a number of factors, in particular seasonality, outlet type, indirect taxation, use of attractive prices as well as aggregate or product-specific inflation.Price-setting ; consumer price ; frequency of price change.

A higher-order entity formed by the flexible assembly of RAP1 with TRF2

Essonne committee of the Ligue contre le cancer M18756 M22897 Foundation ARC pour la Recherche sur le Cancer SFI20121205503International audienceTelomere integrity is essential to maintain genome stability, and telomeric dysfunctions are associated with cancer and aging pathologies. In human, the shelterin complex binds TTAGGG DNA repeats and provides capping to chromosome ends. Within shel-terin, RAP1 is recruited through its interaction with TRF2, and TRF2 is required for telomere protection through a network of nucleic acid and protein interactions. RAP1 is one of the most conserved shelterin proteins although one unresolved question is how its interaction may influence TRF2 properties and regulate its capacity to bind multiple proteins. Through a combination of biochemical, biophysical and structural approaches, we unveiled a unique mode of assembly between RAP1 and TRF2. The complete interaction scheme between the full-length proteins involves a complex biphasic interaction of RAP1 that directly affects the binding properties of the assembly. These results reveal how a non-DNA binding protein can influence the properties of a DNA-binding partner by mutual conformational adjustments

Dual-polarized aperture-coupled patch antennas with application to retrodirective and monopulse arrays

An isolation technique, which does not require conventional circulators, is proposed for the realization of a simple and low-cost aperture-coupled circularly polarized antenna for application to full-duplex devices. The approach is based on the use of slotlines loops to provide surface current cancellation in specific regions of the antenna structure, leading to improved axial ratio and isolation between the ports in excess of 50 dB. Circular polarization is achieved by introducing a double-box hybrid coupler, which is optimized to obtain good matching and isolation of the quadrature signals. On this basis, both right- and left-hand circularly polarized beams are achieved by interchanging the transmitting and receiving antenna ports, enabling full-duplex operation and reconfigurability. While the antenna structure is designed for 2.45 GHz operation, one can take advantage of the proposed approach to tune the frequency of maximum isolation. Both single-element prototypes as well as a 2 × 2 array are fabricated and measured, showing good agreement with the simulations and validating the proposed isolation approach. The beam steering capabilities as well as the application to a Van Atta retrodirective antenna array and the possibilities of achieving delta and sum patterns for monopulse operation are also reported. The proposed full-duplex antenna can also represent an excellent solution for narrowband wireless power transmission systems

Properties of a general quaternion-valued gradient operator and its applications to signal processing

The gradients of a quaternion-valued function are often required for quaternionic signal processing algorithms. The HR gradient operator provides a viable framework and has found a number of applications. However, the applications so far have been limited to mainly real-valued quaternion functions and linear quaternionvalued functions. To generalize the operator to nonlinear quaternion functions, we define a restricted version of the HR operator, which comes in two versions, the left and the right ones. We then present a detailed analysis of the properties of the operators, including several different product rules and chain rules. Using the new rules, we derive explicit expressions for the derivatives of a class of regular nonlinear quaternion-valued functions, and prove that the restricted HR gradients are consistent with the gradients in the real domain. As an application, the derivation of the least mean square algorithm and a nonlinear adaptive algorithm is provided. Simulation results based on vector sensor arrays are presented as an example to demonstrate the effectiveness of the quaternion-valued signal model and the derived signal processing algorithm

Microstructural damage of the posterior corpus callosum contributes to the clinical severity of neglect

One theory to account for neglect symptoms in patients with right focal damage invokes a release of inhibition of the right parietal cortex over the left parieto-frontal circuits, by disconnection mechanism. This theory is supported by transcranial magnetic stimulation studies showing the existence of asymmetric inhibitory interactions between the left and right posterior parietal cortex, with a right hemispheric advantage. These inhibitory mechanisms are mediated by direct transcallosal projections located in the posterior portions of the corpus callosum. The current study, using diffusion imaging and tract-based spatial statistics (TBSS), aims at assessing, in a data-driven fashion, the contribution of structural disconnection between hemispheres in determining the presence and severity of neglect. Eleven patients with right acute stroke and 11 healthy matched controls underwent MRI at 3T, including diffusion imaging, and T1-weighted volumes. TBSS was modified to account for the presence of the lesion and used to assess the presence and extension of changes in diffusion indices of microscopic white matter integrity in the left hemisphere of patients compared to controls, and to investigate, by correlation analysis, whether this damage might account for the presence and severity of patients' neglect, as assessed by the Behavioural Inattention Test (BIT). None of the patients had any macroscopic abnormality in the left hemisphere; however, 3 cases were discarded due to image artefacts in the MRI data. Conversely, TBSS analysis revealed widespread changes in diffusion indices in most of their left hemisphere tracts, with a predominant involvement of the corpus callosum and its projections on the parietal white matter. A region of association between patients' scores at BIT and brain FA values was found in the posterior part of the corpus callosum. This study strongly supports the hypothesis of a major role of structural disconnection between the right and left parietal cortex in determining 'neglect'

The Data Quality Monitoring for the CMS Silicon Strip Tracker

The CMS Silicon Strip Tracker (SST), consisting of more than 10 million channels, is organized in about 15,000 detector modules and it is the largest silicon strip tracker ever built for high energy physics experiments. The Data Quality Monitoring system for the Tracker has been developed within the CMS Software framework. More than 100,000 monitorable quantities need to be managed by the DQM system that organizes them in a hierarchical structure reflecting the detector arrangement in subcomponents and the various levels of data processing. Monitorable quantities computed at the level of individual detectors are processed to extract automatic quality checks and summary results that can be visualized with specialized graphical user interfaces. In view of the great complexity of the CMS Tracker detector the standard visualization tools based on histograms have been complemented with 2 and 3 dimensional graphical images of the subdetector that can show the whole detector down to single channel resolution. The functionalities of the CMS Silicon Strip Tracker DQM system and the experience acquired during the SST commissioning will be described