Inf-semilattice approach to self-dual morphology

Today, the theoretical framework of mathematical morphology is phrased in terms of complete lattices and operators defined on them. That means in particular that the choice of the underlying partial ordering is of eminent importance, as it determines the class of morphological operators that one ends up with. The duality principle for partially ordered sets, which says that the opposite of a partial ordering is also a partial ordering, gives rise to the fact that all morphological operators occur in pairs, e.g., dilation and erosion, opening and closing, etc. This phenomenon often prohibits the construction of tools that treat foreground and background of signals in exactly the same way. In this paper we discuss an alternative framework for morphological image processing that gives rise to image operators which are intrinsically self-dual. As one might expect, this alternative framework is entirely based upon the definition of a new self-dual partial ordering

The Chin as a Domain Widener in American Sign Language (ASL)

In this paper, we investigate a grammaticalized facial expression in American Sign Language (ASL) called flat chin, which we propose functions as a general-purpose domain widener, targeting both quantificational domains as well as the scales used by gradable predicates. Our analysis allows for flat chin to target nearly any expression involving a domain, and is based on Morzycki's (2012) analysis of extreme degree modifiers. Such an analysis both expands our understanding of ASL as well Language more broadly, as few general-purpose domain wideners have yet been reported and fewer still are reported to occur as a non-manual (non-hand) markers in a sign language

Radio spectral study of the cluster of galaxies Abell 2255

Spectral index studies of halos, relics, and radio galaxies provide useful information on their origin and connection with merger processes. We present WSRT multi-wavelength observations of the galaxy cluster Abell 2255 at 25 cm, 85 cm, and 2 m. The spectral index images allowed us to study the integrated spectrum of halo and relic and to investigate the physical properties of the Beaver head-tail radio galaxy belonging to the cluster. In the radio halo, the spectral index is steeper at the center and flatter at the locations of the radio filaments, clearly detected at 25 cm. In the relics, the spectral index flattens, moving away from the cluster center. For the Beaver radio galaxy, the spectrum severely steepens from the head towards the end of the tail, because of the energy losses suffered by the relativistic particles. In the 2 m map, which is the first high-sensitivity image presented in the literature at such a long wavelength, a new Mpc-size emission region is detected between the known radio halo and the NW relic. Not detecting this feature in the more sensitive 85 cm observations implies that it must have a very steep spectrum (alpha <= -2.6). The observational properties of the radio halo suggest that either we are looking at a superposition of different structures (filaments in the foreground plus real halo in the background) seen in projection across the cluster center or that the halo is intrinsically peculiar. The newly detected extended region to the NW of the halo could be considered as an asymmetric extension of the halo itself. However, since radio halos are known in the literature as structures showing a regular morphology, the new feature could represent the first example of steep Mpc-size diffuse structures (MDS), detected around clusters at very low frequencies.Comment: 23 pages, 18 figures. A&A, in pres

Analytical Study of Diffusive Relativistic Shock Acceleration

Particle acceleration in relativistic shocks is studied analytically in the test-particle, small-angle scattering limit, for an arbitrary velocity-angle diffusion function D. Accurate analytic expressions for the spectral index s are derived using few (2-6) low-order moments of the shock-frame angular distribution. For isotropic diffusion, previous results are reproduced and justified. For anisotropic diffusion, s is shown to be sensitive to D, particularly downstream and at certain angles, and a wide range of s values is attainable. The analysis, confirmed numerically, can be used to test collisionless shock models and to observationally constrain D. For example, strongly forward- or backward-enhanced diffusion downstream is ruled out by GRB afterglow observations.Comment: 4 pages, 2 figures, PRL accepted, minor change

Survival Probabilities of History-Dependent Random Walks

We analyze the dynamics of random walks with long-term memory (binary chains with long-range correlations) in the presence of an absorbing boundary. An analytically solvable model is presented, in which a dynamical phase-transition occurs when the correlation strength parameter \mu reaches a critical value \mu_c. For strong positive correlations, \mu > \mu_c, the survival probability is asymptotically finite, whereas for \mu < \mu_c it decays as a power-law in time (chain length).Comment: 3 pages, 2 figure

Self-Similar Collisionless Shocks

Observations of gamma-ray burst afterglows suggest that the correlation length of magnetic field fluctuations downstream of relativistic non-magnetized collisionless shocks grows with distance from the shock to scales much larger than the plasma skin depth. We argue that this indicates that the plasma properties are described by a self-similar solution, and derive constraints on the scaling properties of the solution. For example, we find that the scaling of the characteristic magnetic field amplitude with distance from the shock is B \propto D^{s_B} with -1<s_B<=0, that the spectrum of accelerated particles is dn/dE \propto E^{-2/(s_B+1)}, and that the scaling of the magnetic correlation function is \propto x^{2s_B} (for x>>D). We show that the plasma may be approximated as a combination of two self-similar components: a kinetic component of energetic particles and an MHD-like component representing "thermal" particles. We argue that the latter may be considered as infinitely conducting, in which case s_B=0 and the scalings are completely determined (e.g. dn/dE \propto E^{-2} and B \propto D^0). Similar claims apply to non- relativistic shocks such as in supernova remnants, if the upstream magnetic field can be neglected. Self-similarity has important implications for any model of particle acceleration and/or field generation. For example, we show that the diffusion function in the angle \mu of momentum p in diffusive shock acceleration models must satisfy D_{\mu\mu}(p,D) = D^{-1}D'_{\mu\mu}(p/D), and that a previously suggested model for the generation of large scale magnetic fields through a hierarchical merger of current-filaments should be generalized. A numerical experiment testing our analysis is outlined (Abridged).Comment: 16 pages, 1 figure, accepted for publication in Ap

Ion dynamics and acceleration in relativistic shocks

Ab-initio numerical study of collisionless shocks in electron-ion unmagnetized plasmas is performed with fully relativistic particle in cell simulations. The main properties of the shock are shown, focusing on the implications for particle acceleration. Results from previous works with a distinct numerical framework are recovered, including the shock structure and the overall acceleration features. Particle tracking is then used to analyze in detail the particle dynamics and the acceleration process. We observe an energy growth in time that can be reproduced by a Fermi-like mechanism with a reduced number of scatterings, in which the time between collisions increases as the particle gains energy, and the average acceleration efficiency is not ideal. The in depth analysis of the underlying physics is relevant to understand the generation of high energy cosmic rays, the impact on the astrophysical shock dynamics, and the consequent emission of radiation.Comment: 5 pages, 3 figure

Phase-Transition in Binary Sequences with Long-Range Correlations

Motivated by novel results in the theory of correlated sequences, we analyze the dynamics of random walks with long-term memory (binary chains with long-range correlations). In our model, the probability for a unit bit in a binary string depends on the fraction of unities preceding it. We show that the system undergoes a dynamical phase-transition from normal diffusion, in which the variance D_L scales as the string's length L, into a super-diffusion phase (D_L ~ L^{1+|alpha|}), when the correlation strength exceeds a critical value. We demonstrate the generality of our results with respect to alternative models, and discuss their applicability to various data, such as coarse-grained DNA sequences, written texts, and financial data.Comment: 4 pages, 4 figure

The influence of lexical selection disruptions on articulation

Interactive models of language production predict that it should be possible to observe long-distance interactions; effects that arise at one level of processing influence multiple subsequent stages of representation and processing. We examine the hypothesis that disruptions arising in nonform-based levels of planning—specifically, lexical selection—should modulate articulatory processing. A novel automatic phonetic analysis method was used to examine productions in a paradigm yielding both general disruptions to formulation processes and, more specifically, overt errors during lexical selection. This analysis method allowed us to examine articulatory disruptions at multiple levels of analysis, from whole words to individual segments. Baseline performance by young adults was contrasted with young speakers’ performance under time pressure (which previous work has argued increases interaction between planning and articulation) and performance by older adults (who may have difficulties inhibiting nontarget representations, leading to heightened interactive effects). The results revealed the presence of interactive effects. Our new analysis techniques revealed these effects were strongest in initial portions of responses, suggesting that speech is initiated as soon as the first segment has been planned. Interactive effects did not increase under response pressure, suggesting interaction between planning and articulation is relatively fixed. Unexpectedly, lexical selection disruptions appeared to yield some degree of facilitation in articulatory processing (possibly reflecting semantic facilitation of target retrieval) and older adults showed weaker, not stronger interactive effects (possibly reflecting weakened connections between lexical and form-level representations)