On the Size Complexity of Non-Returning Context-Free PC Grammar Systems

Improving the previously known best bound, we show that any recursively enumerable language can be generated with a non-returning parallel communicating (PC) grammar system having six context-free components. We also present a non-returning universal PC grammar system generating unary languages, that is, a system where not only the number of components, but also the number of productions and the number of nonterminals are limited by certain constants, and these size parameters do not depend on the generated language

Electron-Ion Interaction Effects in Attosecond Time-Resolved Photoelectron Spectra

Photoionization by attosecond (as) extreme ultraviolet (xuv) pulses into the laser-dressed continuum of the ionized atom is commonly described in strong-field approximation (SFA), neglecting the Coulomb interaction between the emitted photoelectron (PE) and residual ion. By solving the time-dependent Sch\"{o}dinger equation (TDSE), we identify a temporal shift $\delta \tau$ in streaked PE spectra, which becomes significant at small PE energies. Within an eikonal approximation, we trace this shift to the combined action of Coulomb and laser forces on the released PE, suggesting the experimental and theoretical scrutiny of their coupling in streaked PE spectra. The initial state polarization effect by the laser pulse on the xuv streaked spectrum is also examined.Comment: 9 pages, Accepted by Phys. Rev.

Serializing the Parallelism in Parallel Communicating Pushdown Automata Systems

We consider parallel communicating pushdown automata systems (PCPA) and define a property called known communication for it. We use this property to prove that the power of a variant of PCPA, called returning centralized parallel communicating pushdown automata (RCPCPA), is equivalent to that of multi-head pushdown automata. The above result presents a new sub-class of returning parallel communicating pushdown automata systems (RPCPA) called simple-RPCPA and we show that it can be written as a finite intersection of multi-head pushdown automata systems

Macroscopic effects in attosecond pulse generation

We examine how the generation and propagation of high-order harmonics in a partly ionized gas medium affect their strength and synchronization. The temporal properties of the resulting attosecond pulses generated in long gas targets can be significantly influenced by macroscopic effects, in particular by the intensity in the medium and the degree of ionization. Under some conditions, the use of gas targets longer than the absorption length can lead to the generation of self-compressed attosecond pulses. We show this effect experimentally, using long argon-filled gas cells as generating medium.Comment: 5 pages 4 figure

A Reconfigurations Analogue of Brooks’ Theorem

Let G be a simple undirected graph on n vertices with maximum degree Δ. Brooks’ Theorem states that G has a Δ-colouring unless G is a complete graph, or a cycle with an odd number of vertices. To recolour G is to obtain a new proper colouring by changing the colour of one vertex. We show that from a k-colouring, k > Δ, a Δ-colouring of G can be obtained by a sequence of O(n 2) recolourings using only the original k colours unless G is a complete graph or a cycle with an odd number of vertices, or k = Δ + 1, G is Δ-regular and, for each vertex v in G, no two neighbours of v are coloured alike. We use this result to study the reconfiguration graph R k (G) of the k-colourings of G. The vertex set of R k (G) is the set of all possible k-colourings of G and two colourings are adjacent if they differ on exactly one vertex. It is known that if k ≤ Δ(G), then R k (G) might not be connected and it is possible that its connected components have superpolynomial diameter, if k ≥ Δ(G) + 2, then R k (G) is connected and has diameter O(n 2). We complete this structural classification by settling the missing case: if k = Δ(G) + 1, then R k (G) consists of isolated vertices and at most one further component which has diameter O(n 2). We also describe completely the computational complexity classification of the problem of deciding whether two k-colourings of a graph G of maximum degree Δ belong to the same component of R k (G) by settling the case k = Δ(G) + 1. The problem is O(n 2) time solvable for k = 3, PSPACE-complete for 4 ≤ k ≤ Δ(G), O(n) time solvable for k = Δ(G) + 1, O(1) time solvable for k ≥ Δ(G) + 2 (the answer is always yes)

Gravitomagnetic Moments and Dynamics of Dirac's (spin 1/2) fermions in flat space-time Maxwellian Gravity

The gravitational effects in the relativistic quantum mechanics are investigated in a relativistically derived version of Heaviside's speculative Gravity (in flat space-time) named here as Maxwellian Gravity. The standard Dirac's approach to the intrinsic spin in the fields of Maxwellian Gravity yields the gravitomagnetic moment of a Dirac (spin 1/2) particle exactly equals to its intrinsic spin. Violation of The Equivalence Principle (both at classical and quantum mechanical level) in the relativistic domain has also been reported in this work.Comment: 27 page

Occupational Therapy Treatment to Improve Upper Extremity Function in Individuals with Early Systemic Sclerosis: A Pilot Study

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/146446/1/acr23522.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/146446/2/acr23522_am.pd

The phase of a quantum mechanical particle in curved spacetime

We investigate the quantum mechanical wave equations for free particles of spin 0,1/2,1 in the background of an arbitrary static gravitational field in order to explicitly determine if the phase of the wavefunction is $S/\hbar = \int p_{\mu} dx^{\mu} / \hbar$, as is often quoted in the literature. We work in isotropic coordinates where the wave equations have a simple managable form and do not make a weak gravitational field approximation. We interpret these wave equations in terms of a quantum mechanical particle moving in medium with a spatially varying effective index of refraction. Due to the first order spatial derivative structure of the Dirac equation in curved spacetime, only the spin 1/2 particle has \textit{exactly} the quantum mechanical phase as indicated above. The second order spatial derivative structure of the spin 0 and spin 1 wave equations yield the above phase only to lowest order in $\hbar$. We develop a WKB approximation for the solution of the spin 0 and spin 1 wave equations and explore amplitude and phase corrections beyond the lowest order in $\hbar$. For the spin 1/2 particle we calculate the phase appropriate for neutrino flavor oscillations.Comment: 30 pages, no figures. Submitted to Gen.Rel.Grav 17 Oct 0

Bounded Languages Meet Cellular Automata with Sparse Communication

Cellular automata are one-dimensional arrays of interconnected interacting finite automata. We investigate one of the weakest classes, the real-time one-way cellular automata, and impose an additional restriction on their inter-cell communication by bounding the number of allowed uses of the links between cells. Moreover, we consider the devices as acceptors for bounded languages in order to explore the borderline at which non-trivial decidability problems of cellular automata classes become decidable. It is shown that even devices with drastically reduced communication, that is, each two neighboring cells may communicate only constantly often, accept bounded languages that are not semilinear. If the number of communications is at least logarithmic in the length of the input, several problems are undecidable. The same result is obtained for classes where the total number of communications during a computation is linearly bounded