Coincidence Set Research Articles

Finitistic spaces with the orbit space 𝔽ℙn × 𝕊m

Let [Formula: see text], [Formula: see text] or [Formula: see text], act freely on a finitistic connected space [Formula: see text]. This paper gives the cohomology classification of [Formula: see text] if the mod 2 or rational cohomology of the orbit space [Formula: see text] is isomorphic to the product of a projective space and sphere [Formula: see text], where [Formula: see text] or [Formula: see text], respectively. For a free involution on [Formula: see text], a lower bound of covering dimension of the coincidence set of a continuous map [Formula: see text] is also determined.

Antarctic polar stratospheric cloud composition as observed by ACE, CALIPSO and MIPAS

The composition of polar stratospheric clouds (PSCs) in the Antarctic is measured by infrared absorption spectroscopy by the Atmospheric Chemistry Experiment (ACE) satellite and compared to lidar (CALIPSO) and emission spectroscopy (MIPAS) results. ACE observations are compared first to CALIPSO for the period 2006–2020, then to MIPAS for the period 2005–2011, and then a set of triple coincidences is studied. In both CALIPSO-ACE and MIPAS-ACE comparisons, nitric acid trihydrate (NAT) detections are in excellent agreement (∼80 % of coincident compositions is found). Supercooled ternary solution (STS) detections are in good agreement for CALIPSO-ACE (∼60 %) but in poor agreement for MIPAS-ACE (39 %). This contrasts with ice detections, in poor agreement for CALIPSO-ACE (∼30 %) and in better agreement for MIPAS-ACE (45 %). Triple coincidences show that ACE STS detections are more reliable than MIPAS STS detections. The comparison between ACE observations and homogeneous CALIPSO PSCs shows that for 11 events, CALIPSO reports STS rather than supercooled nitric acid (SNA) clouds.

Seismic characterization of a fluid escape structure in the North Sea: the Scanner Pockmark complex area

SUMMARYSubsurface fluid escape structures are geological features which are commonly observed in sedimentary basins worldwide. Their identification and description have implications for various subsurface fluid flow applications, such as assuring integrity of overburden rocks to geological CO2 storage sites. In this study, we applied 3-D first-arrival traveltime tomography to a densely sampled wide-azimuth and wide-angle ocean bottom seismometer (OBS) data set collected over the Scanner Pockmark complex, a site of active gas venting in the North Sea. Seismic reflection data show a chimney structure underlying the Scanner Pockmark. The objective of this study was to characterize this chimney as a representative fluid escape structure in the North Sea. An area of 6$\times $6 km2 down to a depth of 2 km below sea level was investigated using a regularized tomography algorithm. In total, 182 069 manually picked traveltimes from 24 OBS were used. Our final velocity model contains compressional wave velocity perturbations ranging from −125 to +110 ms−1 relative to its average 1-D model and compares favourably with a coincident seismic reflection data set. The tomographic velocity model reveals that the chimney as observed in seismic reflection data is part of a larger complex fluid escape structure, and discriminates the genuine chimney from seismic artefacts. We find that part of the seeping gas migrates from a deep source, accumulates beneath the Crenulate Reflector unconformity at ∼250 m below seafloor (mbsf) before reaching the porous sediments of the Ling Bank and Coal Pit formation at <100 mbsf. In addition, the model shows that the venting gas at Scanner Pockmark is also being fed laterally through a narrow NW–SE shallow channel. Quantitative velocity analysis suggests a patchy gas saturation within the gas-charged sediments of the Ling Bank and the Coal Pit formations. Confined to the well-resolved regions, we estimate a base case average gas saturation of ∼9 per cent and in-situ gas volume of ∼1.64 $\times {10^6}\ {{\rm{m}}^3}$ across the Ling Bank and Coal Pit Fm. that can sustain the observed methane flux rate at the Scanner Pockmark for about 10 to 17 yr.

The influence of Xenophon’s didactic writings on the military leadership practice of Alexander the Great

The article examines the influence of Xenophon’s didactic works on the military activities of Alexander the Great. It is re-vealed that messages from ancient sources containing direct in-dications of the fact that Alexander was familiar with Xeno-phon’s works are either fundamentally unreliable or subject to different interpretations. Nevertheless, a comparison of the rec-ommendations proposed in “Kyropedia” and other Athenian au-thor’s writings the with Alexander’s practical activities reveals obvious similarities in their views on training military personnel, organizing competitions in military skill, providing soldiers with richly decorated weapons, and caring for the sick and wounded. A set of coincidences is associated with the political and admin-istrative activities of Alexander, who, like Cyrus the Elder in Xenophon’s writings, demonstratively showed mercy towards the vanquished, attracted representatives of the local elite to the ser-vice, wore clothes traditional for a conquered country. A large number of similarities, good education of Alexander and the popularity of Xenophon’s writings in the second half of the 4th century BCE allow us to conclude that the Macedonian king was familiar with the works of the Athenian author. However, the components of Xenophon's didactic legacy associated with the methods of warfare do not correlate well with Alexander's mili-tary leadership practice. The fundamental differences are re-vealed in the armament of the cavalry and their tactics, the depth of the infantry formation, the role of army branches on the battle-field. They were caused by a significant breakthrough in the art of war that took place in Macedonia during the time of Philip II. This breakthrough also led to the emergence of new tactics that provided for crushing the enemy not with a frontal attack of heavy infantry, but through the combined use of various types of troops. Alexander as a military leader was raised under the con-ditions of a new, more developed military art. Thus, the over-whelming majority of Xenophon's recommendations, which de-scribed the cavalry as a purely auxiliary branch of the army and considered the classical hoplite phalanx a decisive force in battle, were clearly irrelevant for him and therefore ignored.

Characterizing compact coincidence sets in the obstacle problem—a short proof

The objective of this article is to present a concise and easy-to-extend proof of the known fact that coincidence sets of global solutions of the obstacle problem that are bounded and have nonempty interior are ellipsoids.

Characterizing compact coincidence sets in the thin obstacle problem and the obstacle problem for the fractional Laplacian

In this paper we give a full classification of global solutions of the obstacle problem for the fractional Laplacian (including the thin obstacle problem) with compact coincidence set and at most polynomial growth in dimension N≥3. We do this in terms of a bijection onto a set of polynomials describing the asymptotics of the solution. Furthermore we prove that coincidence sets of global solutions that are compact are also convex if the solution has at most quadratic growth.

Biharmonic Obstacle Problem: Guaranteed and Computable Error Bounds for Approximate Solutions

The paper is concerned with a free boundary problem generated by the biharmonic operator and an obstacle. The main goal is to deduce a fully guaranteed upper bound of the difference between the exact minimizer u and any function (approximation) from the corresponding energy class (which consists of the functions in $H^2$ satisfying the prescribed boundary conditions and the restrictions stipulated by the obstacle). For this purpose we use the duality method of the calculus of variations and general type error identities earlier derived for a wide class of convex variational problems. By this method, we define a combined primal--dual measure of error. It contains four terms of different nature. Two of them are the norms of the difference between the exact solutions (of the direct and dual variational problems) and corresponding approximations. Two others are nonlinear measures, related to approximation of the coincidence set (they vanish if the coincidence set defined by means of the approximate solution coincides with the exact one). The measure satisfies the error identity, which right hand side depends on approximate solutions only and, therefore, is fully computable. Thus, the identity provides direct estimation of the primal--dual errors. However, it contains a certain restriction on the form of the dual approximation. In the second part of the paper, we present a way to skip the restriction. As a result, we obtain a fully guaranteed and directly computable error majorant valid for a wide class of approximations regardless of the method used for their construction. The estimates are verified in a series of tests with different approximate solutions. Some of them are quite close to the exact solution and others are rather coarse and have coincidence sets that differ much from the exact one. The results show that the estimates are robust and effective in all the cases.

Three-nucleon dynamics in dp breakup collisions using the WASA detector at COSY-Jülich

Differential cross section for the 1H(d,pp)n breakup reaction at deuteron beam energy of 340 MeV has been measured with the use of WASA detector at COSY-Juelich. The set of proton-proton coincidences registered at Forward Detector has been analysed on dense grid of kinematic variables, giving in total around 5600 data points. The cross section data are compared to theoretical predictions based on the state-of-the-art nucleon-nucleon potentials, combined with three-nucleon force, Coulomb interaction or carried out in a relativistic regime.

Regularity of the Solution of the Scalar Signorini Problem in Polygonal Domains

The Signorini problem for the Laplace operator is considered in a general polygonal domain. It is proved that the coincidence set consists of a finite number of boundary parts plus a finite number of isolated points. The regularity of the solution is described. In particular, we show that the leading singularity is in general $$r_i^{\pi /(2\alpha _i)}$$ at transition points of Signorini to Dirichlet or Neumann conditions but $$r_i^{\pi /\alpha _i}$$ at kinks of the Signorini boundary, with $$\alpha _i$$ being the internal angle of the domain at these critical points.

Coincidence judgment in causal reasoning: How coincidental is this?

Given the important conceptual connections between cause and coincidence as well as the extensive prior research on causality asking, “how causal is this?”, the present research proposes and evaluated a psychological construction of coincidentality as the answer to the question, “how coincidental is this?” Four experiments measured the judgment properties of a reasonably large set of real coincidences from an initial diary study. These judgements included coincidentality and an array of other judgments about event uncertainty, hypothesis belief and surprise as predictors of coincidentality consistent with and supporting our prior definition of coincidence (Johansen & Osman, 2015): “coincidences are surprising pattern repetitions that are observed to be unlikely by chance but are nonetheless ascribed to chance since the search for causal mechanisms has not produced anything more plausible than mere chance.” In particular, we evaluated formal models based on judgements of uncertainty, belief and surprise as predictors to develop a model of coincidentality. Ultimately, we argue that coincidentality is a marker for causal suspicion/discovery in terms of a flag that a new, unknown causal mechanism may be operating.

A stand-alone analysis of quasidensity

In this paper we consider the of a subset of the product of a space and its dual, and give a connection between quasidense and of type (NI). We discuss sets of certain convex functions and prove two sum theorems for coincidence sets. We obtain new results on the Fitzpatrick extension of a closed quasidense monotone multifunction. The analysis in this paper is self-contained, and independent of previous work on Banach SN spaces. This version differs from the previous version because it is shown that the (well known) equivalence of quasidensity and type (NI) for maximally monotone is not true without the monotonicity assumption and that the appendix has been moved to the end of Section 10, where it rightfully belongs.

Analysis of blow-ups for the double obstacle problem in dimension two

In this article we study a normalised double obstacle problem with polynomial obstacles p^1(x)\leq p^2(x) , where the equality holds iff x=0 . In dimension two we give a complete classification of blow-up solutions. In particular, we see that there exists a new type of blow-ups, which we call double-cone solutions, since the coincidence sets \{u=p^1\} and \{u=p^2\} are cones with a common vertex. Furthermore, we show that if the solution to the double obstacle problem has a double-cone blow-up limit at the origin, then the blow-up is unique, and locally the free boundary consists of four C^{1,\gamma} -curves, meeting at the origin.

A harmonized image processing workflow using Sentinel-2/MSI and Landsat-8/OLI for mapping water clarity in optically variable lake systems

This study demonstrates the applicability of harmonizing Sentinel-2 MultiSpectral Imager (MSI) and Landsat-8 Operational Land Imager (OLI) satellite imagery products to enable the monitoring of inland lake water clarity in the Google Earth Engine (GEE) environment. Processing steps include (1) atmospheric correction and masking of MSI and OLI imagery, and (2) generating scene-based water clarity maps in terms of Secchi depth (SD). We adopted ocean-color based atmospheric correction theory for MSI and OLI sensors modified with associated scene-specific metadata and auxiliary datasets available in GEE to generate uniform remote sensing reflectances (Rrs) products over optically variable freshwater lake surfaces. MSI-Rrs products derived from the atmospheric correction were used as input predictors in a bootstrap forest to determine significant band combinations to predict water clarity. A SD model for MSI (SDMSI) was then developed using a calibration dataset consisting of log-transformed SDin situ measurements (lnSDin situ) from 79 optically variable freshwater inland lakes collected within ±1 day of satellite overpass on 23-Aug 2017 (MAE = 0.53 m) and validated with 276 samples collected within ±1 day of a 12-Sep 2017 image (MAE = 0.66 m) across three ecoregions in Minnesota, USA. A separate SD model for MSI was also developed using similar spectral bands present on the OLI sensor (SDsOLI) where cross-sensor performance can be evaluated during coincident overpass events. SDsOLI applied to both MSI and OLI (SDOLI) models were further validated using two coincident overpass sets of imagery on 27-Sep 2017 (n = 18) and 13-Aug 2018 (n = 43), yielding a range of error from 0.25 to 0.67 m. Potential sources of model errors and limitations are discussed. Data derived from this multi-sensor methodology is anticipated to be used by researchers, lake resource managers, and citizens to expedite the pre-processing steps so that actionable information can be retrieved for decision making.

Homogenization of obstacle problems in Orlicz–Sobolev spaces

We study the homogenization of obstacle problems in Orlicz–Sobolev spaces for a wide class of monotone operators (possibly degenerate or singular) of the p(\cdot) -Laplacian type. Our approach is based on the Lewy–Stampacchia inequalities, which then give access to a compactness argument. We also prove the convergence of the coincidence sets under non-degeneracy conditions.

Reidemeister classes for coincidences between sections of a fiber bundle

Let $s_0,f_0$ be two sections of a fiber bundle $q: E\to B$ and the coincidence set $\Gamma(s_0,f_0)\neq \emptyset$. We consider the following question: Is there $s_0\simeq_B s_1$ (by the homotopies which cover the constant homotopy $\overline{I}_B$ on the basic space) such that $\Gamma(s_1, f_0)=\emptyset$? If $b_0\in \Gamma(s_0,f_0)$ and $F_0=q^{-1}(b_0)$ is the typical fiber, in this context we can use the homotopy lifting extension propriety of the fibration $q$ to obtain homotopies over $B$. When we make this and the basic point are fixed we can use the elements $s_0(\beta), f_0(\beta^{-1})$ where $\beta \in\pi_1(B,b_0)$ and the elements $\gamma\in \pi_1(F_0,e_0)$. So we will introduce the algebraic classes of Reidemeister relative to the subgroup $\pi_1(F_0,e_0)$. When the basic points are not fixed we need to consider the classes $[\til{s}]_L$ of lifting of $s_0$ defined on the universal covering $\til{B}$ to $\til{E}$. The present work relates the lifting classes $[\til{s}]_L$ of $s_0$ and the algebraic relative Reidemeister classes $R_A(s_0,f_0; \pi_1(F_0,e_0).$

Lexical Grammar: Activities for Teaching Chunks and Exploring PatternsTeaching Grammar: From Rules to Reasons. Practical Ideas and Advice for Working with Grammar in the Classroom

Two new volumes—both with the word ‘grammar’ in the title. Both written by active teachers and teacher trainers. Both aimed at practising teachers and/or teacher trainers rather than academics. Both are the first book for the two authors (although both have got numerous articles to their name, and Selivan is also an active blogger—cf. http://leoxicon.blogspot.com). Both are written in the wide CLT tradition, and as such adhere to the ‘meaning first’ principle (before any reflection on form), and are generally use-oriented and relatively light on metalinguistic considerations. And, unsurprisingly, both are descriptive rather than prescriptive in their overall approach. All of the above is a nice enough set of coincidences, but the really intriguing parallels between the two volumes lie somewhere else still. Before exploring them more thoroughly, let me first describe the structure and contents of the two books in some detail. Selivan’s volume is the most recent in a series of Cambridge Handbooks for Language Teachers and its design follows the familiar format of these publications. It opens with a brief but dense introductory theoretical chapter, where Selivan calls on a very powerful theoretical apparatus, including seminal contributions in corpus analysis, the lexical approach, lexical priming theory, complexity theory, and usage-based theory of language acquisition to justify his stance. This is followed by ten practical chapters, each of which contains around ten activity descriptions, all aimed at—as the book’s subtitle promises—teaching lexico-grammatical chunks and exploring language patterns. The majority of the activities are pitched at A2+ level or higher and are designed with teenage or (young) adult learners in mind, but there are a few beginner-level activities, some of which are suitable for primary-school learners. Each activity description includes an outline, target learner language level, time to be allocated in the classroom, information on any prior preparation needed, and a full in-class sequence of steps to be taken. Also included are suggestions for variation(s) and/or follow-ups. Many of the activities require access to a device with an internet connection (but not necessarily in class, as many activity variations include alternative homework suggestions).

Indices of a Finitistic Space with Mod 2 Cohomology ℝPn × $$\mathbb{S}^2$$ S 2

Let G = ℤ2 act freely on a finitistic space X with mod 2 cohomology ring isomorphic to the product of a real projective space and 2-sphere $$\mathbb{S}^2$$ . In this paper, we determine the Conner and Floyd’s mod 2 cohomology index and the Volovikov’s numerical index of X. Using these indices, we discuss the nonexistence of equivariant maps $$X\rightarrow\mathbb{S}^n$$ and $$\mathbb{S}^n\rightarrow{X}$$ . The covering dimensions of the coincidence sets of continuous maps X → ℝk are also determined.

Applying deep neural networks to the detection and space parameter estimation of compact binary coalescence with a network of gravitational wave detectors

In this paper, we study an application of deep learning to the advanced LIGO and advanced Virgo coincident detection of gravitational waves (GWs) from compact binary star mergers. This deep learning method is an extension of the Deep Filtering method used by George and Huerta (2017) for multi-inputs of network detectors. Simulated coincident time series data sets in advanced LIGO and advanced Virgo detectors are analyzed for estimating source luminosity distance and sky location. As a classifier, our deep neural network (DNN) can effectively recognize the presence of GW signals when the optimal signal-to-noise ratio (SNR) of network detectors $\geq$ 9. As a predictor, it can also effectively estimate the corresponding source space parameters, including the luminosity distance $D$, right ascension $\alpha$, and declination $\delta$ of the compact binary star mergers. When the SNR of the network detectors is greater than 8, their relative errors are all less than 23%. Our results demonstrate that Deep Filtering can process coincident GW time series inputs and perform effective classification and multiple space parameter estimation. Furthermore, we compare the results obtained from one, two, and three network detectors; these results reveal that a larger number of network detectors results in a better source location.

Directional differentiability for elliptic quasi-variational inequalities of obstacle type

The directional differentiability of the solution map of obstacle type quasi-variational inequalities (QVIs) with respect to perturbations on the forcing term is studied. The classical result of Mignot is then extended to the quasi-variational case under assumptions that allow multiple solutions of the QVI. The proof involves selection procedures for the solution set and represents the directional derivative as the limit of a monotonic sequence of directional derivatives associated to specific variational inequalities. Additionally, estimates on the coincidence set and several simplifications under higher regularity are studied. The theory is illustrated by a detailed study of an application to thermoforming comprising of modelling, analysis and some numerical experiments.

Some remarks on the coincidence set for the Signorini problem

We study some properties of the coincidence set for the boundary Signorini problem, improving some results from previous works by the second author and collaborators. Among other new results, we show here that the convexity assumption on the domain made previously in the literature on the location of the coincidence set can be avoided under suitable alternative conditions on the data.