Topological analysis of scalar fields with outliers

Given a real-valued function $f$ defined over a manifold $M$ embedded in $\mathbb{R}^d$, we are interested in recovering structural information about $f$ from the sole information of its values on a finite sample $P$. Existing methods provide approximation to the persistence diagram of $f$ when geometric noise and functional noise are bounded. However, they fail in the presence of aberrant values, also called outliers, both in theory and practice. We propose a new algorithm that deals with outliers. We handle aberrant functional values with a method inspired from the k-nearest neighbors regression and the local median filtering, while the geometric outliers are handled using the distance to a measure. Combined with topological results on nested filtrations, our algorithm performs robust topological analysis of scalar fields in a wider range of noise models than handled by current methods. We provide theoretical guarantees and experimental results on the quality of our approximation of the sampled scalar field

Search for domain wall dark matter with atomic clocks on board global positioning system satellites

Cosmological observations indicate that 85% of all matter in the Universe is dark matter (DM), yet its microscopic composition remains a mystery. One hypothesis is that DM arises from ultralight quantum fields that form macroscopic objects such as topological defects. Here we use GPS as a ~ 50,000 km aperture DM detector to search for such defects in the form of domain walls. GPS navigation relies on precision timing signals furnished by atomic clocks hosted on board GPS satellites. As the Earth moves through the galactic DM halo, interactions with topological defects could cause atomic clock glitches that propagate through the GPS satellite constellation at galactic velocities ~ 300 km/s. Mining 16 years of archival GPS data, we find no evidence for DM in the form of domain walls at our current sensitivity level. This allows us to improve the limits on certain quadratic scalar couplings of domain wall DM to standard model particles by several orders of magnitude.Comment: 7 pages (main text), and 12 pages for Supplementary Information. v3: Update titl

Urban identity through quantifiable spatial attributes: coherence and dispersion of local identity through the automated comparative analysis of building block plans

This analysis investigates whether and to what degree quantifiable spatial attrib-utes, as expressed in plan representations, can capture elements related to the ex-perience of spatial identity. By combining different methods of shape and spatial analysis it attempts to quantify spatial attributes, predominantly derived from plans, in order to illustrate patterns of interrelations between spaces through an ob-jective automated process. The study focuses on the scale of the urban block as the basic modular unit for the formation of urban configurations and the issue of spa-tial identity is perceived through consistency and differentiation within and amongst urban neighbourhoods

Is there Correlation between Fine Structure and Dark Energy Cosmic Dipoles?

We present a detailed analysis (including redshift tomography) of the cosmic dipoles in the Keck+VLT quasar absorber and in the Union2 SnIa samples. We show that the fine structure constant cosmic dipole obtained through the Keck+VLT quasar absorber sample at $4.1\sigma$ level is anomalously aligned with the corresponding dark energy dipole obtained through the Union2 sample at $2\sigma$ level. The angular separation between the two dipole directions is $11.3^\circ \pm 11.8^\circ$. We use Monte Carlo simulations to find the probability of obtaining the observed dipole magnitudes with the observed alignment, in the context of an isotropic cosmological model with no correlation between dark energy and fine structure constant $\alpha$. We find that this probability is less than one part in $10^6$. We propose a simple physical model (extended topological quintessence) which naturally predicts a spherical inhomogeneous distribution for both dark energy density and fine structure constant values. The model is based on the existence of a recently formed giant global monopole with Hubble scale core which also couples non-minimally to electromagnetism. Aligned dipole anisotropies would naturally emerge for an off-centre observer for both the fine structure constant and for dark energy density. This model smoothly reduces to \lcdm for proper limits of its parameters. Two predictions of this model are (a) a correlation between the existence of strong cosmic electromagnetic fields and the value of $\alpha$ and (b) the existence of a dark flow on Hubble scales due to the repulsive gravity of the global defect core (`Great Repulser') aligned with the dark energy and $\alpha$ dipoles. The direction of the dark flow is predicted to be towards the spatial region of lower accelerating expansion. Existing data about the dark flow are consistent with this prediction.Comment: 14 pages 11 figures (two column revtex). Aceepted in Phys. Rev. D (to appear). Significant extensions (mostly on section 4 on the theoretical model), added references, corrected typos. The data, updated mathematica and C program files used for the numerical analysis may be downloaded from http://leandros.physics.uoi.gr/defsdipole

Spectral comparison of large urban graphs

The spectrum of an axial graph is proposed as a means for comparison between spaces, particularly for measuring between very large and complex graphs. A number of methods have been used in recent years for comparative analysis within large sets of urban areas, both to investigate properties of specific known types of street network or to propose a taxonomy of urban morphology based on an analytical technique. In many cases, a single or small range of predefined, scalar measures such as metric distance, integration, control or clustering coefficient have been used to compare the graphs. While these measures are well understood theoretically, their low dimensionality determines the range of observations that can ultimately be drawn from the data. Spectral analysis consists of a high dimensional vector representing each space, between which metric distance may be measured to indicate the overall difference between two spaces, or subspaces may be extracted to correspond to certain features. It is used for comparison of entire urban graphs, to determine similarities (and differences) in their overall structure. Results are shown of a comparison of 152 cities distributed around the world. The clustering of cities of similar properties in a high dimensional space is discussed. Principal and nonlinear components of the data set indicate significant correlations in the graph similarities between cities and their proximity to one another, suggesting that cultural features based on location are evident in the city form and that these can be quantified by the proposed method. Results of classification tests show that a city’s location can be estimated based purely on its form. The high dimensionality of the spectra is beneficial for its utility in data-mining applications that can draw correlations with other data sets such as land use information. It is shown how further processing by supervised learning allows the extraction of relevant features. A methodological comparison is also drawn with statistical studies that use a strong correlation between human genetic markers and geographical location of populations to derive detailed reconstructions of prehistoric migration. Thus, it is suggested that the method may be utilised for mapping the transfer of cultural memes by measuring comparison between cities

Instanton dominance over αs\alpha_s at low momenta from lattice QCD simulations at Nf=0N_f=0, Nf=2+1N_f=2+1 and Nf=2+1+1N_f=2+1+1

We report on an instanton-based analysis of the gluon Green functions in the Landau gauge for low momenta; in particular we use lattice results for $\alpha_s$ in the symmetric momentum subtraction scheme (${\rm MOM}$) for large-volume lattice simulations. We have exploited quenched gauge field configurations, $N_f=0$, with both Wilson and tree-level Symanzik improved actions, and unquenched ones with $N_f=2+1$ and $N_f=2+1+1$ dynamical flavors (domain wall and twisted-mass fermions, respectively). We show that the dominance of instanton correlations on the low-momenta gluon Green functions can be applied to the determination of phenomenological parameters of the instanton liquid and, eventually, to a determination of the lattice spacing. We furthermore apply the Gradient Flow to remove short-distance fluctuations. The Gradient Flow gets rid of the QCD scale, $\Lambda_{\rm QCD}$, and reveals that the instanton prediction extents to large momenta. For those gauge field configurations free of quantum fluctuations, the direct study of topological charge density shows the appearance of large-scale lumps that can be identified as instantons, giving access to a direct study of the instanton density and size distribution that is compatible with those extracted from the analysis of the Green functions.Comment: Proceedings of the 35th International Symposium on Lattice Field Theory, Granada, Spai

Search for transient ultralight dark matter signatures with networks of precision measurement devices using a Bayesian statistics method

We analyze the prospects of employing a distributed global network of precision measurement devices as a dark matter and exotic physics observatory. In particular, we consider the atomic clocks of the Global Positioning System (GPS), consisting of a constellation of 32 medium-Earth orbit satellites equipped with either Cs or Rb microwave clocks and a number of Earth-based receiver stations, some of which employ highly-stable H-maser atomic clocks. High-accuracy timing data is available for almost two decades. By analyzing the satellite and terrestrial atomic clock data, it is possible to search for transient signatures of exotic physics, such as "clumpy" dark matter and dark energy, effectively transforming the GPS constellation into a 50,000km aperture sensor array. Here we characterize the noise of the GPS satellite atomic clocks, describe the search method based on Bayesian statistics, and test the method using simulated clock data. We present the projected discovery reach using our method, and demonstrate that it can surpass the existing constrains by several order of magnitude for certain models. Our method is not limited in scope to GPS or atomic clock networks, and can also be applied to other networks of precision measurement devices.Comment: See also Supplementary Information located in ancillary file

Intrinsic geometry of collider events and nearest neighbour based weighted filtration

Collider observations have mainly been studied on an event-by-event basis, leveraging several kinematic techniques. However, the intrinsic topological imprints of the ensemble of new physics events can be strikingly different from the SM background ensemble. Traditional topological data analysis (TDA) is known for its stability against small perturbations. However, a plethora of rich information encoded in the clustering of ensembles is often lost due to the unweighted filtration of simplicial complexes. Taking a singlet extended model as an example, this work illustrates the rich global properties associated with the so-called distance-to-measure (DTM) filtration on Alpha complexes using weights determined from k-nearest neighbours.Comment: 1 table, 7 figure