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

Ketamine for Refractory Headache: A Retrospective Analysis.

BACKGROUND AND OBJECTIVES: The burden of chronic headache disorders in the United States is substantial. Some patients are treatment refractory. Ketamine, an N-methyl-D-aspartate antagonist, provides potent analgesia in subanesthetic doses in chronic pain, and limited data suggest it may alleviate headache in some patients. METHODS: We performed a retrospective study of 61 patients admitted over 3 years for 5 days of intravenous therapy that included continuous ketamine to determine responder rate and patient and ketamine infusion characteristics. Pain ratings at 2 follow-up visits were recorded. An immediate responder was a patient with decrease of 2 points or greater in the numerical rating scale (0-10) from start to final pain in the hospital. Sustained response at office visits 1 and 2 was determined based on maintaining the 2-point improvement at those visits. Patients were assessed daily for pain and adverse events (AEs). RESULTS: Forty-eight (77%) of the 61 patients were immediate responders. There were no differences regarding demographics, opioid use, or fibromyalgia between immediate responders and nonresponders. Maximum improvement occurred 4.56 days (mean) into treatment. Sustained response occurred in 40% of patients at visit 1 (mean, 38.1 days) and 39% of patients at visit 2 (mean, 101.3 days). The mean maximum ketamine rate was 65.2 ± 2.8 mg/h (0.76 mg/kg per hour). Ketamine rates did not differ between groups. Adverse events occurred equally in responders and nonresponders and were mild. CONCLUSIONS: Ketamine was associated with short-term analgesia in many refractory headache patients with tolerable adverse events. A prospective study is warranted to confirm this and elucidate responder characteristics

Quaternion Analysis for Generalized Electromagnetic Fields of Dyons in Isotropic Medium

Quaternion analysis of time dependent Maxwell's equations in presence of electric and magnetic charges has been developed and the solutions for the classical problem of moving charges (electric and magnetic) are obtained in unique, simple and consistent manner

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.

Selected amino acid changes in HIV-1 subtype-C gp41 are associated with specific gp120(V3) signatures in the regulation of co-receptor usage

The majority of studies have characterized the tropism of HIV-1 subtype-B isolates, but little is known about the determinants of tropism in other subtypes. So, the goal of the present study was to genetically characterize the envelope of viral proteins in terms of co-receptor usage by analyzing 356 full-length env sequences derived from HIV-1 subtype-C infected individuals. The co-receptor usage of V3 sequences was inferred by using the Geno2Pheno and PSSM algorithms, and also analyzed to the "11/25 rule". All reported env sequences were also analyzed with regard to N-linked glycosylation sites, net charge and hydrophilicity, as well as the binomial correlation phi coefficient to assess covariation among gp120(V3) and gp41 signatures and the average linkage hierarchical agglomerative clustering were also performed. Among env sequences present in Los Alamos Database, 255 and 101 sequences predicted as CCR5 and CXCR4 were selected, respectively. The classical V3 signatures at positions 11 and 25, and other specific V3 and gp41 amino acid changes were found statistically associated with different co-receptor usage. Furthermore, several statistically significant associations between V3 and gp41 signatures were also observed. The dendrogram topology showed a cluster associated with CCR5-usage composed by five gp41 mutated positions, A22V, R133M, E136G, N140L, and N166Q that clustered with T2V(V3) and G24T(V3) (bootstrap=1). Conversely, a heterogeneous cluster with CXCR4-usage, involving S11GR(V3), 13-14insIG/LG(V3), P16RQ(V3), Q18KR(V3), F20ILV(V3), D25KRQ(V3), Q32KR(V3) along with A30T(gp41), S107N(gp41), D148E(gp41), A189S(gp41) was identified (bootstrap=0.86). Our results show that as observed for HIV-1 subtype-B, also in subtype-C specific and different gp41 and gp120V3 amino acid changes are associated individually or together with CXCR4 and/or CCR5 usage. These findings strengthen previous observations that determinants of tropism may also reside in the gp41 protein

The measurement of household consumption expenditures

Household-level data on consumer expenditures underpin a wide range of empirical research in modern economics, spanning micro-and macroeconomics. This research includes work on consumption and saving, on poverty and inequality, and on risk sharing and insurance. We review different ways in which such data can be collected or captured: traditional detailed budget surveys, less onerous survey procedures that might be included in more general surveys, and administrative or process data. We discuss the advantages and difficulties of each approach and suggest directions for future investigation. © 2014 by Annual Reviews. All rights reserved

Prevalence of resistance mutations related to integrase inhibitor S/GSK1349572 in HIV-1 subtype B raltegravir-naive and -treated patients

Objectives To compare the frequency of previously in vitro-selected integrase mutations (T124A, T124A/S153F, S153Y, T124A/S153Y and L101I/T124A/S153Y) conferring resistance to S/GSK1349572 between HIV-1 subtype B integrase inhibitor (INI)-naive and raltegravir-treated patients. Methods Integrase sequences from 650 INI-naive patients and 84 raltegravir-treated patients were analysed. Results The T124A mutation alone and the combination T124A/L101I were more frequent in raltegravir-failing patients than in INI-naive patients (39.3% versus 24.5%, respectively, P = 0.005 for T124A and 20.2% versus 10.0%, respectively, P = 0.008 for T124A/L101I). The S153Y/F mutations were not detected in any integrase sequence (except for S153F alone, only detected in one INI-naive patient). Conclusions T124A and T124A/L101I, more frequent in raltegravir-treated patients, could have some effect on raltegravir response and their presence could play a role in the selection of other mutations conferring S/GSK1349572 resistance. The impact of raltegravir-mediated changes such as these on the virological response to S/GSK1349572 should be studied further

Spacelike distance from discrete causal order

Any discrete approach to quantum gravity must provide some prescription as to how to deduce continuum properties from the discrete substructure. In the causal set approach it is straightforward to deduce timelike distances, but surprisingly difficult to extract spacelike distances, because of the unique combination of discreteness with local Lorentz invariance in that approach. We propose a number of methods to overcome this difficulty, one of which reproduces the spatial distance between two points in a finite region of Minkowski space. We provide numerical evidence that this definition can be used to define a `spatial nearest neighbor' relation on a causal set, and conjecture that this can be exploited to define the length of `continuous curves' in causal sets which are approximated by curved spacetime. This provides evidence in support of the ``Hauptvermutung'' of causal sets.Comment: 32 pages, 16 figures, revtex4; journal versio

Notions of Infinity in Quantum Physics

In this article we will review some notions of infiniteness that appear in Hilbert space operators and operator algebras. These include proper infiniteness, Murray von Neumann's classification into type I and type III factors and the class of F{/o} lner C*-algebras that capture some aspects of amenability. We will also mention how these notions reappear in the description of certain mathematical aspects of quantum mechanics, quantum field theory and the theory of superselection sectors. We also show that the algebra of the canonical anti-commutation relations (CAR-algebra) is in the class of F{/o} lner C*-algebras.Comment: 11 page

Surface plasmons of metallic surfaces perforated by nanoholes

Recent works dealt with the optical transmission on arrays of subwavelength holes perforated in a thick metallic film. We have performed simulations which quantitatively agree with experimental results and which unambiguously evidence that the extraordinary transmission is due to the excitation of a surface-plasmon-polariton (SPP) mode on the metallic film interfaces. We identify this SPP mode and show that its near-field possesses a hybrid character, gathering collective and localised effects which are both essential for the transmission.Comment: 16 pages, 4 figure