Origami constraints on the initial-conditions arrangement of dark-matter caustics and streams

In a cold-dark-matter universe, cosmological structure formation proceeds in rough analogy to origami folding. Dark matter occupies a three-dimensional 'sheet' of free- fall observers, non-intersecting in six-dimensional velocity-position phase space. At early times, the sheet was flat like an origami sheet, i.e. velocities were essentially zero, but as time passes, the sheet folds up to form cosmic structure. The present paper further illustrates this analogy, and clarifies a Lagrangian definition of caustics and streams: caustics are two-dimensional surfaces in this initial sheet along which it folds, tessellating Lagrangian space into a set of three-dimensional regions, i.e. streams. The main scientific result of the paper is that streams may be colored by only two colors, with no two neighbouring streams (i.e. streams on either side of a caustic surface) colored the same. The two colors correspond to positive and negative parities of local Lagrangian volumes. This is a severe restriction on the connectivity and therefore arrangement of streams in Lagrangian space, since arbitrarily many colors can be necessary to color a general arrangement of three-dimensional regions. This stream two-colorability has consequences from graph theory, which we explain. Then, using N-body simulations, we test how these caustics correspond in Lagrangian space to the boundaries of haloes, filaments and walls. We also test how well outer caustics correspond to a Zel'dovich-approximation prediction.Comment: Clarifications and slight changes to match version accepted to MNRAS. 9 pages, 5 figure

Measuring Multijet Structure of Hadronic Energy Flow Or What IS A Jet?

Ambiguities of jet algorithms are reinterpreted as instability wrt small variations of input. Optimal stability occurs for observables possessing property of calorimetric continuity (C-continuity) predetermined by kinematical structure of calorimetric detectors. The so-called C-correlators form a basic class of such observables and fit naturally into QFT framework, allowing systematic theoretical studies. A few rules generate other C-continuous observables. The resulting C-algebra correctly quantifies any feature of multijet structure such as the "number of jets" and mass spectra of "multijet substates". The new observables are physically equivalent to traditional ones but can be computed from final states bypassing jet algorithms which reemerge as a tool of approximate computation of C-observables from data with all ambiguities under analytical control and an optimal recombination criterion minimizing approximation errors.Comment: PostScript, 94 pp (US Letter), 18 PS files, [email protected]

Semantic Interpretation of an Artificial Neural Network

Recent advances in machine learning theory have opened the door for applications to many difficult problem domains. One area that has achieved great success for stock market analysis/prediction is artificial neural networks. However, knowledge embedded in the neural network is not easily translated into symbolic form. Recent research, exploring the viability of merging artificial neural networks with traditional rule-based expert systems, has achieved limited success. In particular, extracting production (IF.. THEN) rules from a trained neural net based on connection weights provides a valid set of rules only when neuron outputs are close to 0 or 1 (e.g. the output sigmoid function is saturated). This thesis presents two new ways to interpret neural network knowledge. The first, called Knowledge Math, extends the use of connection weights, generating rules for general (i.e. non-binary) input and output values. The second method, based on decision boundaries, utilizes the inherent border between output classification regions to draw symbolic interpretation. The Decision Boundary method generates more complex symbolic rules than Knowledge Math, but provides valid feature relationships in the uncertain regions around the midpoints of the neuron output functions. The main result is a complementary relationship between Knowledge Math and Decision Boundaries, as well as subsymbolic and symbolic knowledge representations for a general multi-layer perceptron

Non-Euclidean geometry in nature

I describe the manifestation of the non-Euclidean geometry in the behavior of collective observables of some complex physical systems. Specifically, I consider the formation of equilibrium shapes of plants and statistics of sparse random graphs. For these systems I discuss the following interlinked questions: (i) the optimal embedding of plants leaves in the three-dimensional space, (ii) the spectral statistics of sparse random matrix ensembles.Comment: 52 pages, 21 figures, last section is rewritten, a reference to chaotic Hamiltonian systems is adde

High-resolution and high-accuracy topographic and transcriptional maps of the nucleosome barrier.

Nucleosomes represent mechanical and energetic barriers that RNA Polymerase II (Pol II) must overcome during transcription. A high-resolution description of the barrier topography, its modulation by epigenetic modifications, and their effects on Pol II nucleosome crossing dynamics, is still missing. Here, we obtain topographic and transcriptional (Pol II residence time) maps of canonical, H2A.Z, and monoubiquitinated H2B (uH2B) nucleosomes at near base-pair resolution and accuracy. Pol II crossing dynamics are complex, displaying pauses at specific loci, backtracking, and nucleosome hopping between wrapped states. While H2A.Z widens the barrier, uH2B heightens it, and both modifications greatly lengthen Pol II crossing time. Using the dwell times of Pol II at each nucleosomal position we extract the energetics of the barrier. The orthogonal barrier modifications of H2A.Z and uH2B, and their effects on Pol II dynamics rationalize their observed enrichment in +1 nucleosomes and suggest a mechanism for selective control of gene expression

Untersuchung von Biopolymereigenschaften mittels Fluoreszenzkorrelationsspektroskopie und computergestützter Methoden

Barsch H. Investigation of biopolymer properties with combined fluorescence correlation spectroscopic and computational methods. Bielefeld (Germany): Bielefeld University; 2008.Neue Erkenntnisse bezüglich der Polymerstruktur von Poly-L-prolinen und einzelsträngigen Polythyminen in wässriger Lösung werden in dieser Arbeit präsentiert. Die Kombination von zeitkorrelierter Einzelphotonenregistrierung (TCSPC) und Fluoreszenzkorrelationsspektroskopie (FCS) von mit Fluoreszenzfarbstoffen markierten Polyprolinderivaten, F-(Pro)N-Trp (mit N = 2 - 10 und F = MR113, MR121, R6G), legen nahe, dass Sub-Populationen der Polyproline mit verringertem Endabstand existieren. Diese Endabstände wurden ebenfalls mittels vereinfachter Molekülmechanik-Simulationen für verschiedene Isomere der Polyproline vorausgesagt. Durch Einbringen von vereinzelten cis-Bindungen in die Prolinpolymere kann gezeigt werden, dass trans-cis-Isomerisierung die Endabstände eines Polymers deutlich verringern kann. Diese Endabstandsverkürzung entspricht den experimentell beobachteten Sub-Populationen, welche bei FCS-Messungen erhöhte Löschung durch photoinduzierten Elektronentransfer ermittelt wurden. Mit einem Fluoreszenzfarbstoff markierte, einzelsträngige Polythymine, MR121-(dT)N (mit N = 2 - 100), wurden durch FCS und moleküldynamische Simulationen untersucht. Die spektroskopischen Messungen liefern längenabhängige hydrodynamische Radien der Polythyminproben, deren Abhängigkeit durch ein Potenzgesetz mit einem Exponenten von 0,5 - 0,7 von der Ionenstärke, I, des Lösungsmittels abhängen. Die Persistenzlänge von MR121-(dT)100, Lp, wurde berechnet und zeigt die Abhängigkeit Lp = I^m mit m = -0,22 ± 0,01. Der Vergleich mit moleküldynamischen Simulationen verschiedener markierter und unmarkierter Polythyminderivate zeigt, dass sich Polythymine wie semiflexible Polmere verhalten, dass für Kettenmoleküle mit einer Länge von N > 30 der Einfluss der Farbstoffmarkierung vernachlässigbar ist und dass elektrostatische Wechselwirkungen bei einer Natriumchlorid-Konzentration von 100 mM vollständig abgeschirmt sind. Weiterhin zeigten die Simulationen, dass die statische Flexibilität der Polythymine durch sterische und geometrische Einschränkungen limitiert ist, was durch eine intrinsische Persistenzlänge von 1,7 nm ausgedrückt werden kann.This thesis presents new insights into the structure of poly-L-proline and single-stranded polythymine polymers in aqueous solution. The combination of time-correlated single-photon counting (TCSPC) and fluorescence correlation spectroscopy (FCS) of fluorescently labeled polyproline derivatives, F-(Pro)N-Trp (with N = 2 - 10 and F = MR113, MR121, R6G), suggest that subpopulations of polyprolines with a reduced end-to-end distance exist. End-to-end distances have also been predicted for different isomers of polyprolines by means of simplified molecular mechanics simulations. Incorporating interspersed cis-bonds into the polyproline shows that trans-cis isomerization leads to significantly shorter end-to-end distances. This fits the experimental results of subpopulations with increased photoinduced electron transfer quenching observed in fluorescent correlation spectroscopy experiments. Fluorescently labeled single-stranded polythymines, MR121-(dT)N (with N = 2 - 100), have been investigated through FCS and molecular dynamics simulations. The spectroscopic measurements resulted in length-dependent hydrodynamic radii of the polythymine probes, which scale according to a power law with an exponent of 0.5 - 0.7 dependent on ionic strength, I, of the solvent. The persistence length of MR121-(dT)100, Lp, has been evaluated which shows a dependence of Lp = I^m with m = - 0.22 ± 0.01. The comparison to molecular dynamics simulations of various labeled and unlabeled polythymine derivatives revealed a semiflexible polymer behavior with neglectable influence of the fluorescent label for polymers with N > 30 and that electrostatic interactions are completely shielded at sodium chloride concentrations of 100 mM. Furthermore, simulation results showed polythymine's static flexibility to be limited by steric and geometric constraints which can be expressed by an intrinsic persistence length of 1.7 nm