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More than half of the volume of our Universe is occupied by cosmic voids. The lensing magnification effect from those under-dense regions is generally thought to give a small dimming contribution: objects on the far side of a void are…

An explicit Wigner formulation of Minkowski particle states for non-inertial observers is unknown. Here, we derive a general prescription to compute the characteristic function for Minkowski-Fock states in accelerated frames. For the…

In this paper, position vector of a spacelike general helix with respect to standard frame in Minkowski space E$^3_1$ are studied in terms of Frenet equations. First, a vector differential equation of third order is constructed to determine…

Particle filtering is a popular method for inferring latent states in stochastic dynamical systems, whose theoretical properties have been well studied in machine learning and statistics communities. In many control problems, e.g.,…

I present a way to visualize the concept of curved spacetime. The result is a curved surface with local coordinate systems (Minkowski Systems) living on it, giving the local directions of space and time. Relative to these systems, special…

Plane arrangements are a useful tool for surface and volume modelling. However, their main drawback is poor scalability. We introduce two key novelties that enable the construction of plane arrangements for complex objects and entire…

In this thesis, I go through the well-known solutions to the one and two-particle systems trapped in a quantum harmonic oscillator and then continue to the three, four and many-body quantum systems. This is done by developing new analytical…

We introduce a method where particle physics processes in cosmology may be calculated by the usual perturbative flat space quantum field theory through an effective Minkowski space description at small time intervals provided that the…

Optics of metamaterials is shown to provide interesting table top models of many non-trivial space-time metrics. The range of possibilities is broader than the one allowed in classical general relativity. For example, extraordinary waves in…

We analyze a boarding solution for a transport system in which the number of passengers allowed to enter a transport cabin is automatically controlled. Expressions charac- terizing the stochastic properties of the passenger queue length,…

We study the geometry of curves in the Minkowski space and in the de Sitter space, specially at points where the tangent direction is lightlike (i.e. has length zero) called lightlike points of the curve. We define the focal sets of these…

In this paper, we study generalized versions of the k-center problem, which involves finding k circles of the smallest possible equal radius that cover a finite set of points in the plane. By utilizing the Minkowski gauge function, we…

We can think of a lensed quasar as taking the Hubble time, shrinking it by \~10^{-11}, and then presenting the result to us as a time delay; the shrinking factor is of the order of fractional sky-area that the lens occupies. This cute fact…

Zonotopes are becoming an increasingly popular set representation for formal verification techniques. This is mainly due to their efficient representation and their favorable computational complexity of important operations in…

This letter casts the problem of optimum discrete beamforming as the computation of the Minkowski sum of convex polygons, which is itself a convex polygon. The number of vertices of the latter is at most the sum of the number of vertices of…

This survey article reviews recent results on fermion system in discrete space-time and corresponding systems in Minkowski space. After a basic introduction to the discrete setting, we explain a mechanism of spontaneous symmetry breaking…

Airport security queues often suffer from inefficiencies that result in long wait times and decreased throughput, especially at peak departure time, affecting both passengers and airlines. This work addresses the problem of reassigning…

The nonlinear stability of Minkowski spacetime has been one of the central achievements in the mathematical theory of general relativity and, more broadly, in the analysis of nonlinear geometric wave equations. Since the seminal work of…

In this paper, position vectors of a time-like curve with respect to standard frame of Minkowski space E$^3_1$ are studied in terms of Frenet equations. First, we prove that position vector of every time-like space curve in Minkowski space…

Superluminal particles are not excluded by particle physics. The apparent Lorentz invariance of the laws of physics does not imply that space-time is indeed minkowskian. Matter made of solutions of Lorentz-invariant equations would feel a…