An explicit compact universal space for real flows

The Kakutani–Bebutov Theorem (1968) states that any compact metric real flow whose fixed point set is homeomorphic to a subset of $\mathbb{R}$ embeds into the Bebutov flow, the $\mathbb{R}$-shift on $C(\mathbb{R},[0,1])$. An interesting fact is that this universal space is a function space. However, it is not compact, nor locally compact. We construct an explicit countable product of compact subspaces of the Bebutov flow which is a universal space for all compact metric real flows, with no restriction; namely, into which any compact metric real flow embeds. The result is compared to previously known universal spaces.     

Bifunctional Nanoscale Assemblies: Multistate Electrochromics Coupled with Charge Trapping and Release

We demonstrate controlled charge trapping and release, accompanied by multiple color changes in a metallo‐organic bilayer. The dual functionality of the metallo‐organic materials provides fundamental insight into the metal‐mediated electron transport pathways. The electrochemical processes are visualized by distinct, four color‐to‐color transitions: red, transparent, orange, and brown. The bilayer is composed of two elements: 1) a nanoscale gate consisting of a layer of well‐defined polypyridyl ruthenium complexes bound to a flexible transparent electrode, and 2) a charge storage layer consisting of isostructural iron complexes attached to the surface of the gate. This gate mediates or blocks electron transport in response to an applied voltage. The charge storage and release depend on the oxidation state of the layer of ruthenium complexes (=gate). Combining electrochemistry with optical data revealed mechanistic information: the brown coloration of the bilayer directly relates to the formation of intermediate ruthenium species, providing evidence for catalytic positive charge release mediated through the gate.     

Representation of the voice onset time (VOT) speech parameter in population responses within primary auditory cortex of the awake monkey

Voice onset time (VOT) signifies the interval between consonant onset and the start of rhythmic vocal-cord vibrations. Differential perception of consonants such as /d/ and /t/ is categorical in American English, with the boundary generally lying at a VOT of 20-40 ms. This study tests whether previously identified response patterns that differentially reflect VOT are maintained in large-scale population activity within primary auditory cortex (A1) of the awake monkey. Multiunit activity and current source density patterns evoked by the syllables /da/ and /ta/ with variable VOTs are examined. Neural representation is determined by the tonotopic organization. Differential response patterns are restricted to lower best-frequency regions. Response peaks time-locked to both consonant and voicing onsets are observed for syllables with a 40- and 60-ms VOT, whereas syllables with a 0- and 20-ms VOT evoke a single response time-locked only to consonant onset. Duration of aspiration noise is represented in higher best-frequency regions. Representation of VOT and aspiration noise in discrete tonotopic areas of A1 suggest that integration of these phonetic cues occurs in secondary areas of auditory cortex. Findings are consistent with the evolving concept that complex stimuli are encoded by synchronized activity in large-scale neuronal ensembles.     

On processes which cannot be distinguished by finite observation

A function J defined on a family C of stationary processes is finitely observable if there is a sequence of functions s _n such that s _n (x ₁,…, x _n ) → J(X) in probability for every process X=(x _n ) ∈ C. Recently, Ornstein and Weiss proved the striking result that if C is the class of aperiodic ergodic finite valued processes, then the only finitely observable isomorphism invariant defined on C is entropy [8]. We sharpen this in several ways. Our main result is that if X → Y is a zero-entropy extension of finite entropy ergodic systems and C is the family of processes arising from generating partitions of X and Y, then every finitely observable function on C is constant. This implies Ornstein and Weiss’ result, and extends it to many other families of processes, e.g., it follows that there are no nontrivial finitely observable isomorphism invariants for processes arising from the class of Kronecker systems, the class of mild mixing zero entropy systems, or the class of strong mixing zero entropy systems. It also follows that for the class of processes arising from irrational rotations, every finitely observable isomorphism invariant must be constant for rotations belonging to a set of full Lebesgue measure. This research was supported by the Israel Science Foundation (grant No. 1333/04)     

Time reversal in dynamically tuned zero-gap periodic systems

We show that short pulses propagating in zero-gap periodic systems can be reversed with 100% efficiency by using weak nonadiabatic tuning of the wave velocity at time scales that can be much slower than the period. Unlike previous schemes, we demonstrate reversal of broadband (few cycle) pulses with simple structures. Our scheme may thus open the way to time reversal in a variety of systems for which it was not accessible before.     

An integral model structure and truncation theory for coherent group actions

In this work we study the homotopy theory of coherent group actions from a global point of view, where we allow both the group and the space acted upon to vary. Using the model of Segal group actions and the model categorical Grothendieck construction we construct a model category encompassing all Segal group actions simultaneously. We then prove a global rectification result in this setting. We proceed to develop a general truncation theory for the model-categorical Grothendieck construction and apply it to the case of Segal group actions. We give a simple characterization of n-truncated Segal group actions and show that every Segal group action admits a convergent Postnikov tower built out of its n-truncations.     

The percolation staircase model and its manifestation in composite materials

We studied the tunneling percolation conductivity dependence on the site or bond occupation probability in the square lattice. The model predicts that in both, lattice and continuum systems in which there is a hierarchy of the local conductances, the dependence of the global conductivity on the site or volume occupation probability will yield a conductivity staircase. In particular we evaluate the implications of the staircase on the critical behavior of the conductivity. We then show experimental evidence for the predicted percolation-tunneling staircase in a Ag-Al₂O₃ granular metal system and in a carbon black-polymer composite. Following that, we propose that for carbon nanotube (CNT) polymer composites the data in the literature give ample support to a percolation-dispersion staircase behavior. The implication of the present findings on the percolation-hopping problem in composite materials is also discussed.