Modified Regge calculus as an explanation of dark energy

Using Regge calculus, we construct a Regge differential equation for the time evolution of the scale factor $a(t)$ in the Einstein-de Sitter cosmology model (EdS). We propose two modifications to the Regge calculus approach: 1) we allow the graphical links on spatial hypersurfaces to be large, as in direct particle interaction when the interacting particles reside in different galaxies, and 2) we assume luminosity distance $D_L$ is related to graphical proper distance $D_p$ by the equation $D_L = (1+z)\sqrt{\overrightarrow{D_p}\cdot \overrightarrow{D_p}}$, where the inner product can differ from its usual trivial form. The modified Regge calculus model (MORC), EdS and $\Lambda$CDM are compared using the data from the Union2 Compilation, i.e., distance moduli and redshifts for type Ia supernovae. We find that a best fit line through $\displaystyle \log{(\frac{D_L}{Gpc})}$ versus $\log{z}$ gives a correlation of 0.9955 and a sum of squares error (SSE) of 1.95. By comparison, the best fit $\Lambda$CDM gives SSE = 1.79 using $H_o$ = 69.2 km/s/Mpc, $\Omega_{M}$ = 0.29 and $\Omega_{\Lambda}$ = 0.71. The best fit EdS gives SSE = 2.68 using $H_o$ = 60.9 km/s/Mpc. The best fit MORC gives SSE = 1.77 and $H_o$ = 73.9 km/s/Mpc using $R = A^{-1}$ = 8.38 Gcy and $m = 1.71\times 10^{52}$ kg, where $R$ is the current graphical proper distance between nodes, $A^{-1}$ is the scaling factor from our non-trival inner product, and $m$ is the nodal mass. Thus, MORC improves EdS as well as $\Lambda$CDM in accounting for distance moduli and redshifts for type Ia supernovae without having to invoke accelerated expansion, i.e., there is no dark energy and the universe is always decelerating.Comment: 15 pages text, 6 figures. Revised as accepted for publication in Class. Quant. Gra

Expansive actions on uniform spaces and surjunctive maps

We present a uniform version of a result of M. Gromov on the surjunctivity of maps commuting with expansive group actions and discuss several applications. We prove in particular that for any group $\Gamma$ and any field \K, the space of $\Gamma$-marked groups $G$ such that the group algebra \K[G] is stably finite is compact.Comment: 21 page

Maxwell equations in matrix form, squaring procedure, separating the variables, and structure of electromagnetic solutions

The Riemann -- Silberstein -- Majorana -- Oppenheimer approach to the Maxwell electrodynamics in vacuum is investigated within the matrix formalism. The matrix form of electrodynamics includes three real 4 \times 4 matrices. Within the squaring procedure we construct four formal solutions of the Maxwell equations on the base of scalar Klein -- Fock -- Gordon solutions. The problem of separating physical electromagnetic waves in the linear space \lambda_{0}\Psi^{0}+\lambda_{1}\Psi^{1}+\lambda_{2}\Psi^{2}+ lambda_{3}\Psi^{3} is investigated, several particular cases, plane waves and cylindrical waves, are considered in detail.Comment: 26 pages 16 International Seminar NCPC, May 19-22, 2009, Minsk, Belaru

Von Neumann Regular Cellular Automata

For any group $G$ and any set $A$, a cellular automaton (CA) is a transformation of the configuration space $A^G$ defined via a finite memory set and a local function. Let $\text{CA}(G;A)$ be the monoid of all CA over $A^G$. In this paper, we investigate a generalisation of the inverse of a CA from the semigroup-theoretic perspective. An element $\tau \in \text{CA}(G;A)$ is von Neumann regular (or simply regular) if there exists $\sigma \in \text{CA}(G;A)$ such that $\tau \circ \sigma \circ \tau = \tau$ and $\sigma \circ \tau \circ \sigma = \sigma$, where $\circ$ is the composition of functions. Such an element $\sigma$ is called a generalised inverse of $\tau$. The monoid $\text{CA}(G;A)$ itself is regular if all its elements are regular. We establish that $\text{CA}(G;A)$ is regular if and only if $\vert G \vert = 1$ or $\vert A \vert = 1$, and we characterise all regular elements in $\text{CA}(G;A)$ when $G$ and $A$ are both finite. Furthermore, we study regular linear CA when $A= V$ is a vector space over a field $\mathbb{F}$; in particular, we show that every regular linear CA is invertible when $G$ is torsion-free elementary amenable (e.g. when $G=\mathbb{Z}^d, \ d \in \mathbb{N}$) and $V=\mathbb{F}$, and that every linear CA is regular when $V$ is finite-dimensional and $G$ is locally finite with $\text{Char}(\mathbb{F}) \nmid o(g)$ for all $g \in G$.Comment: 10 pages. Theorem 5 corrected from previous versions, in A. Dennunzio, E. Formenti, L. Manzoni, A.E. Porreca (Eds.): Cellular Automata and Discrete Complex Systems, AUTOMATA 2017, LNCS 10248, pp. 44-55, Springer, 201

Helicity, polarization, and Riemann-Silberstein vortices

Riemann-Silberstein (RS) vortices have been defined as surfaces in spacetime where the complex form of a free electromagnetic field given by F=E+iB is null (F.F=0), and they can indeed be interpreted as the collective history swept out by moving vortex lines of the field. Formally, the nullity condition is similar to the definition of "C-lines" associated with a monochromatic electric or magnetic field, which are curves in space where the polarization ellipses degenerate to circles. However, it was noted that RS vortices of monochromatic fields generally oscillate at optical frequencies and are therefore unobservable while electric and magnetic C-lines are steady. Here I show that under the additional assumption of having definite helicity, RS vortices are not only steady but they coincide with both sets of C-lines, electric and magnetic. The two concepts therefore become one for waves of definite frequency and helicity. Since the definition of RS vortices is relativistically invariant while that of C-lines is not, it may be useful to regard the vortices as a wideband generalization of C-lines for waves of definite helicity.Comment: 5 pages, no figures. Submitted to J of Optics A, special issue on Singular Optics; minor changes from v.

Neoadjuvant treatment of Dermatofibrosarcoma Protuberans of pancreas with Imatinib: case report and systematic review of literature

Abstract Dermatofibrosarcoma Protuberans (DFSP) is a rare skin tumor, characterized by frequent local recurrence but is seldom metastatic. It is histologically characterized by storiform arrangement of spindle cells. Cytogenetically, most tumors are characterized by translocation 17:22 leading to overexpression of tyrosine kinase PDGFB which can be targeted with tyrosine kinase inhibitor, Imatinib. We describe the first case of unresectable pancreatic metastases from DFSP treated with neoadjuvant Imatinib and subsequently R0 metastectomy. Additionally, a comprehensive systematic review of DFSP pancreatic metastases and the current published data on the use of Imatinib in DFSP is summarized.Peer Reviewe

Sustained Activation of Cell Adhesion Is a Differentially Regulated Process in B Lymphopoiesis

It is largely unknown how hematopoietic progenitors are positioned within specialized niches of the bone marrow microenvironment during development. Chemokines such as CXCL12, previously called stromal cell–derived factor 1, are known to activate cell integrins of circulating leukocytes resulting in transient adhesion before extravasation into tissues. However, this short-term effect does not explain the mechanism by which progenitor cells are retained for prolonged periods in the bone marrow. Here we show that in human bone marrow CXCL12 triggers a sustained adhesion response specifically in progenitor (pro- and pre-) B cells. This sustained adhesion diminishes during B cell maturation in the bone marrow and, strikingly, is absent in circulating mature B cells, which exhibit only transient CXCL12-induced adhesion. The duration of adhesion is tightly correlated with CXCL12-induced activation of focal adhesion kinase (FAK), a known molecule involved in integrin-mediated signaling. Sustained adhesion of progenitor B cells is associated with prolonged FAK activation, whereas transient adhesion in circulating B cells is associated with short-lived FAK activation. Moreover, sustained and transient adhesion responses are differentially affected by pharmacological inhibitors of protein kinase C and phosphatidylinositol 3-kinase. These results provide a developmental cell stage–specific mechanism by which chemokines orchestrate hematopoiesis through sustained rather than transient activation of adhesion and cell survival pathways

Shift-Symmetric Configurations in Two-Dimensional Cellular Automata: Irreversibility, Insolvability, and Enumeration

The search for symmetry as an unusual yet profoundly appealing phenomenon, and the origin of regular, repeating configuration patterns have long been a central focus of complexity science and physics. To better grasp and understand symmetry of configurations in decentralized toroidal architectures, we employ group-theoretic methods, which allow us to identify and enumerate these inputs, and argue about irreversible system behaviors with undesired effects on many computational problems. The concept of so-called configuration shift-symmetry is applied to two-dimensional cellular automata as an ideal model of computation. Regardless of the transition function, the results show the universal insolvability of crucial distributed tasks, such as leader election, pattern recognition, hashing, and encryption. By using compact enumeration formulas and bounding the number of shift-symmetric configurations for a given lattice size, we efficiently calculate the probability of a configuration being shift-symmetric for a uniform or density-uniform distribution. Further, we devise an algorithm detecting the presence of shift-symmetry in a configuration. Given the resource constraints, the enumeration and probability formulas can directly help to lower the minimal expected error and provide recommendations for system's size and initialization. Besides cellular automata, the shift-symmetry analysis can be used to study the non-linear behavior in various synchronous rule-based systems that include inference engines, Boolean networks, neural networks, and systolic arrays.Comment: 22 pages, 9 figures, 2 appendice