Resonances, Unstable Systems and Irreversibility: Matter Meets Mind

The fundamental time-reversal invariance of dynamical systems can be broken in various ways. One way is based on the presence of resonances and their interactions giving rise to unstable dynamical systems, leading to well-defined time arrows. Associated with these time arrows are semigroups bearing time orientations. Usually, when time symmetry is broken, two time-oriented semigroups result, one directed toward the future and one directed toward the past. If time-reversed states and evolutions are excluded due to resonances, then the status of these states and their associated backwards-in-time oriented semigroups is open to question. One possible role for these latter states and semigroups is as an abstract representation of mental systems as opposed to material systems. The beginnings of this interpretation will be sketched.Comment: 9 pages. Presented at the CFIF Workshop on TimeAsymmetric Quantum Theory: The Theory of Resonances, 23-26 July 2003, Instituto Superior Tecnico, Lisbon, Portugal; and at the Quantum Structures Association Meeting, 7-22 July 2004, University of Denver. Accepted for publication in the Internation Journal of Theoretical Physic

The Significance of William Augustus Bowles’s Seizure of Panton’s Apalachee Store in 1792

William Augustus Bowles accompanied by William Cunningham and a band of Indians made up of Cowitas, Broken Arrows, Hitchetas, Ufales, Chichas, and Ousutches captured the Apalachee trading post of Panton, Leslie and Company on the 16th day of January 1792. This event was one of the most important incidents in the commercial warfare waged by the merchants of New Providence against the house of Panton

In vivo analysis of NHPX reveals a novel nucleolar localization pathway involving a transient accumulation in splicing speckles

The NHPX protein is a nucleolar factor that binds directly to a conserved RNA target sequence found in nucleolar box C/D snoRNAs and in U4 snRNA. Using enhanced yellow fluorescent protein (EYFP)– and enhanced cyan fluorescent protein–NHPX fusions, we show here that NHPX is specifically accumulated in both nucleoli and Cajal bodies (CBs) in vivo. The fusion proteins display identical localization patterns and RNA binding specificities to the endogenous NHPX. Analysis of a HeLa cell line stably expressing EYFP–NHPX showed that the nucleolar accumulation of NHPX was preceded by its transient accumulation in splicing speckles. Only newly expressed NHPX accumulated in speckles, and the nucleolar pool of NHPX did not interchange with the pool in speckles, consistent with a unidirectional pathway. The transient accumulation of NHPX in speckles prior to nucleoli was observed in multiple cell lines, including primary cells that lack CBs. Inhibitor studies indicated that progression of newly expressed NHPX from speckles to nucleoli was dependent on RNA polymerase II transcription, but not on RNA polymerase I activity. The data show a specific temporal pathway involving the sequential and directed accumulation of NHPX in distinct subnuclear compartments, and define a novel mechanism for nucleolar localization

Homotopy classification of ribbon tubes and welded string links

Ribbon 2-knotted objects are locally flat embeddings of surfaces in 4-space which bound immersed 3-manifolds with only ribbon singularities. They appear as topological realizations of welded knotted objects, which is a natural quotient of virtual knot theory. In this paper we consider ribbon tubes and ribbon torus-links, which are natural analogues of string links and links, respectively. We show how ribbon tubes naturally act on the reduced free group, and how this action classifies ribbon tubes up to link-homotopy, that is when allowing each component to cross itself. At the combinatorial level, this provides a classification of welded string links up to self-virtualization. This generalizes a result of Habegger and Lin on usual string links, and the above-mentioned action on the reduced free group can be refined to a general "virtual extension" of Milnor invariants. As an application, we obtain a classification of ribbon torus-links up to link-homotopy.Comment: 33p. ; v2: typos and minor corrections ; v3: Introduction rewritten, exposition revised, references added. Section 5 of the previous version was significantly expanded and was separated into another paper (arXiv:1507.00202) ; v4: typos and minor corrections ; to appear in Annali della scuola Normale Superiore de Pisa (classe de scienze

Stable quasicrystalline ground states

We give a strong evidence that noncrystalline materials such as quasicrystals or incommensurate solids are not exceptions but rather are generic in some regions of a phase space. We show this by constructing classical lattice-gas models with translation-invariant, finite-range interactions and with a unique quasiperiodic ground state which is stable against small perturbations of two-body potentials. More generally, we provide a criterion for stability of nonperiodic ground states.Comment: 14 pages, Latex, 10 figures available upon request, completely revised versio