The Energy-Momentum tensor on SpincSpin^c manifolds

On $Spin^c$ manifolds, we study the Energy-Momentum tensor associated with a spinor field. First, we give a spinorial Gauss type formula for oriented hypersurfaces of a $Spin^c$ manifold. Using the notion of generalized cylinders, we derive the variationnal formula for the Dirac operator under metric deformation and point out that the Energy-Momentum tensor appears naturally as the second fundamental form of an isometric immersion. Finally, we show that generalized $Spin^c$ Killing spinors for Codazzi Energy-Momentum tensor are restrictions of parallel spinors.Comment: To appear in IJGMMP (International Journal of Geometric Methods in Modern Physics), 22 page

Optimal eigenvalues estimate for the Dirac operator on domains with boundary

We give a lower bound for the eigenvalues of the Dirac operator on a compact domain of a Riemannian spin manifold under the \MIT bag boundary condition. The limiting case is characterized by the existence of an imaginary Killing spinor.Comment: 10 page

How to find the holonomy algebra of a Lorentzian manifold

Manifolds with exceptional holonomy play an important role in string theory, supergravity and M-theory. It is explained how one can find the holonomy algebra of an arbitrary Riemannian or Lorentzian manifold. Using the de~Rham and Wu decompositions, this problem is reduced to the case of locally indecomposable manifolds. In the case of locally indecomposable Riemannian manifolds, it is known that the holonomy algebra can be found from the analysis of special geometric structures on the manifold. If the holonomy algebra $\mathfrak{g}\subset\mathfrak{so}(1,n-1)$ of a locally indecomposable Lorentzian manifold $(M,g)$ of dimension $n$ is different from $\mathfrak{so}(1,n-1)$, then it is contained in the similitude algebra $\mathfrak{sim}(n-2)$. There are 4 types of such holonomy algebras. Criterion how to find the type of $\mathfrak{g}$ are given, and special geometric structures corresponding to each type are described. To each $\mathfrak{g}$ there is a canonically associated subalgebra $\mathfrak{h}\subset\mathfrak{so}(n-2)$. An algorithm how to find $\mathfrak{h}$ is provided.Comment: 15 pages; the final versio

Constraints on Deflation from the Equation of State of Dark Energy

In cyclic cosmology based on phantom dark energy the requirement that our universe satisfy a CBE-condition ({\it Comes Back Empty}) imposes a lower bound on the number $N_{\rm cp}$ of causal patches which separate just prior to turnaround. This bound depends on the dark energy equation of state $w = p/\rho = -1 - \phi$ with $\phi > 0$. More accurate measurement of $\phi$ will constrain $N_{\rm cp}$. The critical density $\rho_c$ in the model has a lower bound $\rho_c \ge (10^9 {\rm GeV})^4$ or $\rho_c \ge (10^{18} {\rm GeV})^4$ when the smallest bound state has size $10^{-15}$m, or $10^{-35}$m, respectively.Comment: 23 pages, 3 figures, typos fixe

Spinorial Characterizations of Surfaces into 3-dimensional pseudo-Riemannian Space Forms

We give a spinorial characterization of isometrically immersed surfaces of arbitrary signature into 3-dimensional pseudo-Riemannian space forms. For Lorentzian surfaces, this generalizes a recent work of the first author in $\mathbb{R}^{2,1}$ to other Lorentzian space forms. We also characterize immersions of Riemannian surfaces in these spaces. From this we can deduce analogous results for timelike immersions of Lorentzian surfaces in space forms of corresponding signature, as well as for spacelike and timelike immersions of surfaces of signature (0,2), hence achieving a complete spinorial description for this class of pseudo-Riemannian immersions.Comment: 9 page

Behavioral, perceptual, and neural alterations in sensory and multisensory function in autism spectrum disorder.

Although sensory processing challenges have been noted since the first clinical descriptions of autism, it has taken until the release of the fifth edition of the Diagnostic and Statistical Manual of Mental Disorders (DSM-5) in 2013 for sensory problems to be included as part of the core symptoms of autism spectrum disorder (ASD) in the diagnostic profile. Because sensory information forms the building blocks for higher-order social and cognitive functions, we argue that sensory processing is not only an additional piece of the puzzle, but rather a critical cornerstone for characterizing and understanding ASD. In this review we discuss what is currently known about sensory processing in ASD, how sensory function fits within contemporary models of ASD, and what is understood about the differences in the underlying neural processing of sensory and social communication observed between individuals with and without ASD. In addition to highlighting the sensory features associated with ASD, we also emphasize the importance of multisensory processing in building perceptual and cognitive representations, and how deficits in multisensory integration may also be a core characteristic of ASD

Handwritten digit recognition by bio-inspired hierarchical networks

The human brain processes information showing learning and prediction abilities but the underlying neuronal mechanisms still remain unknown. Recently, many studies prove that neuronal networks are able of both generalizations and associations of sensory inputs. In this paper, following a set of neurophysiological evidences, we propose a learning framework with a strong biological plausibility that mimics prominent functions of cortical circuitries. We developed the Inductive Conceptual Network (ICN), that is a hierarchical bio-inspired network, able to learn invariant patterns by Variable-order Markov Models implemented in its nodes. The outputs of the top-most node of ICN hierarchy, representing the highest input generalization, allow for automatic classification of inputs. We found that the ICN clusterized MNIST images with an error of 5.73% and USPS images with an error of 12.56%

Density Waves Instability and a Skyrmion Lattice on the Surface of Strong Topological Insulators

In this work we analyze the instability conditions for spin-density-waves (SDW) formation on the surface of strong topological insulators. We find that for a certain range of Fermi-energies and strength of interactions the SDW state is favored compared to the unmagnetized and the uniform-magnetization states. We also find that the SDW are of spiral nature and for a certain range of parameters a Skyrmion-lattice may form on the surface. We show that this phase may have a non trivial Chern-number even in the absence of an external magnetic field.Comment: 6 pages, 7 figure

Probing Ionization Energies for Trace Gas Identification: The Micro Photo Electron Ionization Detector (PEID)

Micro gas sensors detect the presence of substances, but can hardly identify them. We developed a novel approach of probing referenceable ionization energies. It extends the photoionization principle towards tunable energies via replacement of photons by accelerated photo electrons. The device comprises UV-LED illumination, an atmospherically stable photoelectron emission layer with a nano-vacuum electronics accelerator realized in thin film technology and charged particle measurement. A voltage variation at the accelerator provides electrons of tunable energies. We were able to prove that variable electron energies can be used for substance detection. The resulting system reaches ambient conditions operability. The actual limitations and challenges are discussed