Space-time Events Research Articles

Exposing Digital Image Forgeries by Illumination Color Classification

For decades, photographs have been used to document space-time events and they have often served as evidence in courts. Although photographers are able to create composites of analog pictures, this process is very time consuming and requires expert knowledge. Today, however, powerful digital image editing software makes image modifications straightforward. This undermines our trust in photographs and, in particular, questions pictures as evidence for real-world events. In this paper, we analyze one of the most common forms of photographic manipulation, known as image composition or splicing. We propose a forgery detection method that exploits subtle inconsistencies in the color of the illumination of images. Our approach is machine-learning-based and requires minimal user interaction. The technique is applicable to images containing two or more people and requires no expert interaction for the tampering decision. To achieve this, we incorporate information from physics- and statistical-based illuminant estimators on image regions of similar material. From these illuminant estimates, we extract texture- and edge-based features which are then provided to a machine-learning approach for automatic decision-making. The classification performance using an SVM meta-fusion classifier is promising. It yields detection rates of 86% on a new benchmark dataset consisting of 200 images, and 83% on 50 images that were collected from the Internet.

Electrostatics in Stueckelberg-Horwitz electrodynamics

In this paper, we study fundamental aspects of electrostatics as a special case in Stueckelberg-Horwitz electromagnetic theory. In this theory, spacetime events xμ(τ) evolve in an unconstrained 8-dimensional phase space, interacting through five τ-dependent gauge fields induced by the current densities associated with their evolutions. The chronological time τ was introduced as an independent evolution parameter in order to free the laboratory clock x0 to evolve alternately 'forward' and 'backward' in time according to the sign of the energy, thus providing a classical implementation of the Feynman-Stueckelberg interpretation of pair creation/annihilation. The resulting theory differs in its underlying mechanics from conventional electromagnetism, but coincides with Maxwell theory in an equilibrium limit.After a brief review of Stueckelberg-Horwitz electrodynamics, we obtain the field produced by an event in uniform motion and verify that it satisfies the field equations. We study this field in the rest frame of the event, where it depends explicitly on coordinate time x0 and the parameter τ, as well as spatial distance R. Calculating with this generalized Coulomb field, we demonstrate how Gauss's theorem and Stoke's theorem apply in 4D spacetime, and obtain the fields associated with a charged line and a charged sheet. Finally, we use the field of the charged sheet to study a static event in the vicinity of a potential barrier. In all of these cases, we observe a small transfer of mass from the field to the particle. It is seen that for an event in the field of an oppositely charged sheet of sufficient density, the event can reverse time direction, providing a specific model for pair phenomena.

Strong lensing, plane gravitational waves and transient flashes

Plane-symmetric gravitational waves are considered as gravitational lenses. Numbers of images, frequency shifts, mutual angles, and image distortion parameters are computed exactly in essentially all non-singular plane wave spacetimes. For a fixed observation event in a particular plane wave spacetime, the number of regular images is found to be the same for almost every pointlike source. This number can be any positive integer, including infinity. Wavepackets of finite width are discussed in detail as well as waves which maintain a constant amplitude for all time. Short wavepackets are found to generically produce up to two images of each source which appear (separately) only some time after the wave has passed. They are initially infinitely bright, infinitely blueshifted images of the infinitely distant past. Later, these images become dim and acquire a rapidly-increasing redshift. For sufficiently weak wavepackets, one such ‘flash’ almost always exists. The appearance of a second flash requires that the Ricci tensor inside the wave exceed a certain threshold. This might occur if a gravitational plane wave is sourced by, e.g., a sufficiently strong electromagnetic plane wave.

Extended Linear and Nonlinear Lorentz Transformations and Superluminality

Two broad scenarios for extended linear Lorentz transformations (ELTs) are modeled in Section 2 for mixing subluminal and superluminal sectors resulting in standard or deformed energy-momentum dispersions. 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What goes in the making of the ELT in this scenario is not the boost speed <svg style="vertical-align:-0.1638pt;width:7.4875002px;" id="M4" height="7.9124999" version="1.1" viewBox="0 0 7.4875002 7.9124999" width="7.4875002" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(.017,-0,0,-.017,.062,7.638)"><use xlink:href="#x1D463"/></g> </svg>, as ascertained by two inertial observers in uniform relative motion (URM), but <svg style="vertical-align:-3.56265pt;width:55.049999px;" id="M5" height="16.6625" version="1.1" viewBox="0 0 55.049999 16.6625" width="55.049999" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(.017,-0,0,-.017,.062,12.162)"><use xlink:href="#x1D463"/></g><g transform="matrix(.017,-0,0,-.017,11.197,12.162)"><path id="xD7" d="M528 54l-36 -38l-198 201l-198 -201l-36 38l197 200l-197 201l36 38l198 -202l198 202l36 -38l-197 -201z" /></g><g transform="matrix(.017,-0,0,-.017,24.949,12.162)"><use xlink:href="#x1D453"/></g><g transform="matrix(.017,-0,0,-.017,35.862,12.162)"><use xlink:href="#x28"/></g><g transform="matrix(.017,-0,0,-.017,41.743,12.162)"><use xlink:href="#x1D463"/></g><g transform="matrix(.017,-0,0,-.017,49.104,12.162)"><use xlink:href="#x29"/></g> </svg>. The second scenario infers the preexistence of two rest-mass-dependent superluminal speeds whereby the ELTs are finite at the light speed <svg style="vertical-align:-0.1638pt;width:7.0250001px;" id="M6" height="7.9499998" version="1.1" viewBox="0 0 7.0250001 7.9499998" width="7.0250001" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(.017,-0,0,-.017,.062,7.675)"><use xlink:href="#x1D450"/></g> </svg>. Particle energies are evaluated in this scenario at <svg style="vertical-align:-0.1638pt;width:7.0250001px;" id="M7" height="7.9499998" version="1.1" viewBox="0 0 7.0250001 7.9499998" width="7.0250001" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(.017,-0,0,-.017,.062,7.675)"><use xlink:href="#x1D450"/></g> </svg> for several particles, including the neutrinos, and are auspiciously found to be below the GKZ energy cutoff and in compliance with a host of worldwide ultrahigh energy cosmic ray data. Section 3 presents two broad scenarios involving a number of novel nonlinear LTs (NLTs) featuring small Lorentz invariance violations (LIVs), as well as resurrecting the notion of simultaneity for limited spacetime events as perceived by two observers in URM. These inquiries corroborate that NLTs could be potent tools for investigating LIVs past the customary LTs.

Nonparametric Bayesian Segmentation of a Multivariate Inhomogeneous Space-Time Poisson Process

A nonparametric Bayesian model is proposed for segmenting time-evolving multivariate spatial point process data. An inhomogeneous Poisson process is assumed, with a logistic stick-breaking process (LSBP) used to encourage piecewise-constant spatial Poisson intensities. The LSBP explicitly favors spatially contiguous segments, and infers the number of segments based on the observed data. The temporal dynamics of the segmentation and of the Poisson intensities are modeled with exponential correlation in time, implemented in the form of a first-order autoregressive model for uniformly sampled discrete data, and via a Gaussian process with an exponential kernel for general temporal sampling. We consider and compare two different inference techniques: a Markov chain Monte Carlo sampler, which has relatively high computational complexity; and an approximate and efficient variational Bayesian analysis. The model is demonstrated with a simulated example and a real example of space-time crime events in Cincinnati, Ohio, USA.

Electric charge in the field of a magnetic event in three-dimensional spacetime

We analyze the motion of an electric charge in the field of a magnetically charged event in three-dimensional spacetime. We start by exhibiting a first integral of the equations of motion in terms of the three conserved components of the spacetime angular momentum, and then proceed numerically. After crossing the light cone of the event, an electric charge initially at rest starts rotating and slowing down. There are two lengths appearing in the problem: (i) the characteristic length $\frac{qg}{2\ensuremath{\pi}m}$, where $q$ and $m$ are the electric charge and mass of the particle, and $g$ is the magnetic charge of the event; and (ii) the spacetime impact parameter ${r}_{0}$. For ${r}_{0}\ensuremath{\gg}\frac{qg}{2\ensuremath{\pi}m}$, after a time of order ${r}_{0}$, the particle makes sharply a quarter of a turn and comes to rest at the same spatial position at which the event happened in the past. This jump is the main signature of the presence of the magnetic event as felt by an electric charge. A derivation of the expression for the angular momentum that uses Noether's theorem in the magnetic representation is given in the Appendix.

Black Hole Horizons and How They Begin

AbstractProperties of black holes are examined that follow from the definition of the horizon as the boundary of the past of null infinity. The beginning of the black hole is defined as the set of spacetime events at which the null geodesics that generate the horizon enter the horizon. This set is spacelike and appears as a crease in the horizon because at least two generators cross at each of its points. The relation between the crease set and future null infinity is that between object and image produced by the gravitational lensing of the collapsing mass-energy. The crease set is not a manifold but has the structure of a tree. Near a vertex the horizon is a cone over a polyhedron.

RELATIVE LOCALITY: A DEEPENING OF THE RELATIVITY PRINCIPLE

We describe a recently introduced principle of relative locality which we propose governs a regime of quantum gravitational phenomena accessible to experimental investigation. This regime comprises phenomena in which ℏ and GN may be neglected, while their ratio, the Planck mass [Formula: see text], is important. We propose that Mp governs the scale at which momentum space may have a curved geometry. We find that there are striking consequences for the concept of locality. The description of events in spacetime now depends on the energy used to probe it. But there remains an invariant description of physics in phase space. There is furthermore a reasonable expectation that the geometry of momentum space can be measured experimentally using astrophysical observations.

Measuring emission coordinates in a pulsar-based relativistic positioning system

A relativistic deep space positioning system has been proposed using four or more pulsars with stable repetition rates. (Each pulsar emits pulses at a fixed repetition period in its rest frame.) The positioning system uses the fact that an event in spacetime can be fully described by emission coordinates: the proper emission time of each pulse measured at the event. The proper emission time of each pulse from four different pulsars---interpolated as necessary---provides the four spacetime coordinates of the reception event in the emission coordinate system. If more than four pulsars are available, the redundancy can improve the accuracy of the determination and/or resolve degeneracies resulting from special geometrical arrangements of the sources and the event. We introduce a robust numerical approach to measure the emission coordinates of an event in any arbitrary spacetime geometry. Our approach uses a continuous solution of the eikonal equation describing the backward null cone from the event. The pulsar proper time at the instant the null cone intersects the pulsar world line is one of the four required coordinates. The process is complete (modulo degeneracies) when four pulsar world lines have been crossed by the light cone. The numerical method is applied in two different examples: measuring emission coordinates of an event in Minkowski spacetime using pulses from four pulsars stationary in the spacetime; and measuring emission coordinates of an event in Schwarzschild spacetime using pulses from four pulsars freely falling toward a static black hole. These numerical simulations are merely exploratory, but with improved resolution and computational resources the method can be applied to more pertinent problems. For instance one could measure the emission coordinates, and therefore the trajectory, of the Earth.

Ut pictura poesis: intermedialnost med tradicionalnim vizualnim pesništvom in sodobno digitalno poezijo

This article discusses the concept of intermediality, comparing traditional visual poetry and contemporary digital poetry. It shows that today’s somewhat fashionable concept of intermediality can actually be traced in the transposition of the classic concept of intertextuality from philosophical discourse, especially as developed by Barthes and Kristeva, to the domain of mediological discourse. The article briefly summarizes the tradition of visual poetry from antiquity to modernism, emphasizing its structure as basically concrete; that is, it implies a material and medial component of language or writing (écriture). This structure calls attention to its self-referential and referential aspect. The digital poetry that continues the line of development of concrete poetry, as it appeared in the 1950s and 1960s, belongs to a broader area of new media poetry that includes any experimental poetry that uses the “new” media. The problematic concept of intermediality can best be explored in a digital environment such as the holographic poetry (or holopoetry) of the noted and versatile contemporary Brazilian artist Eduardo Kac. Kac’s holopoetry is a special space-time event in the context of the holographic projection of the text in order to display its multilinearity, which primarily means breaking with the linearity of classic poetry printed in a book. Based on an examination of Kac’s holopoem “Havoc” from 1992 (in this example, the poem’s graphic integrity is temporarily lost), the paper challenges the simplistic deconstructivist interpretation that is applied to Kac’s poems and often to digital poetry in general: namely, that these poetic events can most persuasively be seen as figures for the unattainability of “pure” presence/absence, materiality/immateriality, reality/virtuality, and so on. The author argues that the “polluted” reading as a reading against metaphysics and tradition in the case of new-media poetry is unconvincing because the visually evident and naïve representation of a (would-be) Derridaean différance is nothing more and nothing less than the Baudrillardean simulacrum: an imaginary representation of the unreal. The author concludes by suggesting that the basic intermedial problems of contemporary digital poetry remain the same as in traditional visual poetry; that is, that they are only reproduced in the new media environment. Their new “materiality” and the extensive possibilities of technical manipulations that they offer should not deceive us that they ipso facto imply completely new ontological dimensions.

Ut pictura poesis: intermedialnost med tradicionalnim vizualnim pesništvom in sodobno digitalno poezijo

This article discusses the concept of intermediality, comparing traditional visual poetry and contemporary digital poetry. It shows that today’s somewhat fashionable concept of intermediality can actually be traced in the transposition of the classic concept of intertextuality from philosophical discourse, especially as developed by Barthes and Kristeva, to the domain of mediological discourse. The article briefly summarizes the tradition of visual poetry from antiquity to modernism, emphasizing its structure as basically concrete; that is, it implies a material and medial component of language or writing (écriture). This structure calls attention to its self-referential and referential aspect. The digital poetry that continues the line of development of concrete poetry, as it appeared in the 1950s and 1960s, belongs to a broader area of new media poetry that includes any experimental poetry that uses the “new” media. The problematic concept of intermediality can best be explored in a digital environment such as the holographic poetry (or holopoetry) of the noted and versatile contemporary Brazilian artist Eduardo Kac. Kac’s holopoetry is a special space-time event in the context of the holographic projection of the text in order to display its multilinearity, which primarily means breaking with the linearity of classic poetry printed in a book. Based on an examination of Kac’s holopoem “Havoc” from 1992 (in this example, the poem’s graphic integrity is temporarily lost), the paper challenges the simplistic deconstructivist interpretation that is applied to Kac’s poems and often to digital poetry in general: namely, that these poetic events can most persuasively be seen as figures for the unattainability of “pure” presence/absence, materiality/immateriality, reality/virtuality, and so on. The author argues that the “polluted” reading as a reading against metaphysics and tradition in the case of new-media poetry is unconvincing because the visually evident and naïve representation of a (would-be) Derridaean différance is nothing more and nothing less than the Baudrillardean simulacrum: an imaginary representation of the unreal. The author concludes by suggesting that the basic intermedial problems of contemporary digital poetry remain the same as in traditional visual poetry; that is, that they are only reproduced in the new media environment. Their new “materiality” and the extensive possibilities of technical manipulations that they offer should not deceive us that they ipso facto imply completely new ontological dimensions.

Relative locality: a deepening of the relativity principle

We describe a recently introduced principle of relative locality which we propose governs a regime of quantum gravitational phenomena accessible to experimental investigation. This regime comprises phenomena in which $${\hbar}$$ and G N may be neglected, while their ratio, the Planck mass $${M_p =\sqrt{\hbar / G_N}}$$ , is important. We propose that M p governs the scale at which momentum space may have a curved geometry. We find that there are striking consequences for the concept of locality. The description of events in spacetime now depends on the energy used to probe it. But there remains an invariant description of physics in phase space. There is furthermore a reasonable expectation that the geometry of momentum space can be measured experimentally using astrophysical observations.

Lorentz covariant formulation for the laws of physics &amp;ndash; particle and elastic body dynamics

An equation representing a law of physics is said to be Lorentz covariant if it can be written in terms of Lorentz covariant quantities. The key property of Lorentz covariant equations is that if they hold in one inertial frame, then they hold in any inertial frame. This condition is a requirement according to the principle of relativity, that is, all non-gravitational laws must make the same predictions for identical experiments taking place at the same space-time event in two different inertial frames of reference. We divided the presentation into three main sections: introduction for a simple case, the analysis of complex motion under electromagnetic Lorentz force in particle accelerators and we end with a covariant formulation for the Hooke law.

A Survey on Geometric Dynamics of 4-Walker Manifold

A Walker n-manifold is a semi-Riemannian n-manifold, which admits a field of parallel null r-planes, with r ≤ 2/n . It is well-known that semi-Riemannian geometry has an important tool to describe spacetime events. Therefore, solutions of some structures about 4-Walker manifold can be used to explain spacetime singularities. Then, here we present complex and paracomplex analogues of Lagrangian and Hamiltonian mechanical systems on 4-Walker manifold. Finally, the geometrical-physical results related to complex (paracomplex) mechanical systems are also discussed.

When action is not least for orbits in general relativity

In Newtonian mechanics, the action for a true trajectory between two spacetime events A and B is a minimum if the final event B occurs before the kinetic focus of the initial event A; otherwise, the action is a saddle point. We give a simplified proof of an analogous theorem in differential geometry for worldlines in a curved spacetime. We locate the kinetic focus for orbits in a Schwarzschild field in the lowest-order post-Newtonian approximation and show that the kinetic focus is shifted beyond its Newtonian value of one angular cycle by a fractional amount of order O(v2/c2).

Visualising Crime Clusters in a Space-time Cube: An Exploratory Data-analysis Approach Using Space-time Kernel Density Estimation and Scan Statistics

For an effective interpretation of spatio-temporal patterns of crime clusters/hotspots, we explore the possibility of three-dimensional mapping of crime events in a space-time cube with the aid of space-time variants of kernel density estimation and scan statistics. Using the crime occurrence dataset of snatch-and-run offences in Kyoto City from 2003 to 2004, we confirm that the proposed methodology enables simultaneous visualisation of the geographical extent and duration of crime clusters, by which stable and transient space-time crime clusters can be intuitively differentiated. Also, the combined use of the two statistical techniques revealed temporal inter-cluster associations showing that transient clusters alternatively appeared in a pair of hotspot regions, suggesting a new type of “displacement” phenomenon of crime. Highlighting the complementary aspects of the two space-time statistical approaches, we conclude that combining these approaches in a space-time cube display is particularly valuable for a spatio-temporal exploratory data analysis of clusters to extract new knowledge of crime epidemiology from a data set of space-time crime events.

Time Functions as Utilities

Every time function on spacetime gives a (continuous) total preordering of the spacetime events which respects the notion of causal precedence. The problem of the existence of a (semi-)time function on spacetime and the problem of recovering the causal structure starting from the set of time functions are studied. It is pointed out that these problems have an analog in the field of microeconomics known as utility theory. In a chronological spacetime the semi-time functions correspond to the utilities for the chronological relation, while in a K-causal (stably causal) spacetime the time functions correspond to the utilities for the K + relation (Seifert’s relation). By exploiting this analogy, we are able to import some mathematical results, most notably Peleg’s and Levin’s theorems, to the spacetime framework. As a consequence, we prove that a K-causal (i.e. stably causal) spacetime admits a time function and that the time or temporal functions can be used to recover the K + (or Seifert) relation which indeed turns out to be the intersection of the time or temporal orderings. This result tells us in which circumstances it is possible to recover the chronological or causal relation starting from the set of time or temporal functions allowed by the spacetime. Moreover, it is proved that a chronological spacetime in which the closure of the causal relation is transitive (for instance a reflective spacetime) admits a semi-time function. Along the way a new proof avoiding smoothing techniques is given that the existence of a time function implies stable causality, and a new short proof of the equivalence between K-causality and stable causality is given which takes advantage of Levin’s theorem and smoothing techniques.

H.E.L.P: A GIS-based Health Exploratory AnaLysis Tool for Practitioners

The last two decades have been characterized by a growing number of Geographical Information System (GIS) applications to the field of health science. From a decision-making and policy perspective, undeniable benefits of GIS include the assessment of health needs and delivery of services, and also the appropriate allocation of workforce and prevention resources. Despite these attractive attributes, the literature suggests that there has been limited GIS uptake among health care decision makers. This paper presents a GIS-based Health Exploratory and anaLysis tool for Practitioners (H.E.L.P.) for the analysis and visualization of space-time point events, applied to hospital patients. H.E.L.P. is viewed as a spatial decision support system which provides a set of powerful analytical tools integrating the computational capabilities of Matlab with the visualization and database functionalities of GIS. The system outputs improve the understanding of disease dynamics and provide resources for decision-makers in allocating appropriate staffing. As an example, H.E.L.P. is applied to a dataset of hospital patients in Cali, Colombia.

Predicting avian distributions to evaluate spatiotemporal overlap with locust control operations in eastern Australia

Locusts and grasshoppers cause considerable economic damage to agriculture worldwide. The Australian Plague Locust Commission uses multiple pesticides to control locusts in eastern Australia. Avian exposure to agricultural pesticides is of conservation concern, especially in the case of rare and threatened species. The aim of this study was to evaluate the probability of pesticide exposure of native avian species during operational locust control based on knowledge of species occurrence in areas and times of application. Using presence-absence data provided by the Birds Australia Atlas for 1998 to 2002, we developed a series of generalized linear models to predict avian occurrences on a monthly basis in 0.5 degrees grid cells for 280 species over 2 million km2 in eastern Australia. We constructed species-specific models relating occupancy patterns to survey date and location, rainfall, and derived habitat preference. Model complexity depended on the number of observations available. Model output was the probability of occurrence for each species at times and locations of past locust control operations within the 5-year study period. Given the high spatiotemporal variability of locust control events, the variability in predicted bird species presence was high, with 108 of the total 280 species being included at least once in the top 20 predicted species for individual space-time events. The models were evaluated using field surveys collected between 2000 and 2005, at sites with and without locust outbreaks. Model strength varied among species. Some species were under- or over-predicted as times and locations of interest typically did not correspond to those in the prediction data set and certain species were likely attracted to locusts as a food source. Field surveys demonstrated the utility of the spatially explicit species lists derived from the models but also identified the presence of a number of previously unanticipated species. These results also emphasize the need for special consideration of rare and threatened species that are poorly predicted by presence-absence models. This modeling exercise was a useful a priori approach in species risk assessments to identify species present at times and locations of locust control applications, and to discover gaps in our knowledge and need for further focused data collection.

Signature-change events in emergent spacetimes with anisotropic scaling

We investigate the behaviour of quantum fields coupled to a spacetime geometry exhibiting finite regions of Euclidean (Riemannian) signature. Although from a gravity perspective this situation might seem somewhat far fetched, we will demonstrate its direct physical relevance for an explicitly realizable condensed matter system whose linearized perturbations experience an effective emergent spacetime geometry with externally controllable signature. This effective geometry is intrinsically quantum in origin, and its signature is determined by the details of the microscopic structure. At the level of the effective field theory arising from our condensed matter system we encounter explicit anisotropic scaling in time and space. Here Lorentz symmetry is an emergent symmetry in the infrared. This anisotropic scaling of time and space cures some of the technical problems that arise when working within a canonical quantisation scheme obeying strict Lorentz invariance at all scales, and so is helpful in permitting signature change events to take place.