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.     

Mean dimension of $${\mathbb{Z}^k}$$-actions

Mean dimension is a topological invariant for dynamical systems that is meaningful for systems with infinite dimension and infinite entropy. Given a \({\mathbb{Z}^k}\)-action on a compact metric space X, we study the following three problems closely related to mean dimension.

1. (1)
   When is X isomorphic to the inverse limit of finite entropy systems?
    
2. (2)
   Suppose the topological entropy \({h_{\rm top}(X)}\) is infinite. How much topological entropy can be detected if one considers X only up to a given level of accuracy? How fast does this amount of entropy grow as the level of resolution becomes finer and finer?
    
3. (3)
   When can we embed X into the \({\mathbb{Z}^k}\)-shift on the infinite dimensional cube \({([0,1]^D)^{\mathbb{Z}^k}}\)?
    

These were investigated for \({\mathbb{Z}}\)-actions in Lindenstrauss (Inst Hautes Études Sci Publ Math 89:227–262, 1999), but the generalization to \({\mathbb{Z}^k}\) remained an open problem. When X has the marker property, in particular when X has a completely aperiodic minimal factor, we completely solve (1) and a natural interpretation of (2), and give a reasonably satisfactory answer to (3).A key ingredient is a new method to continuously partition every orbit into good pieces.     

Frequency conversion in novel materials and its application to high resolution gas sensing

We have constructed a compact room-temperature mid-infrared spectrometer and gas sensor, based on quasi-phase matched difference-frequency generation in periodically poled ferroelectric crystals of the KTiOPO₄ family, namely: KTiOPO₄, KTiOAsO₄ and RbTiOAsO₄. The wide tunabilty of the spectrometer (3.1–3.75 μm) enables us to cover an entire vibrational band of gases such as methane and nitrous oxide. The high spectral resolution (1 MHz) is used to investigate the spectral profile of the hyperfine components of a single rotational transition. The sensitivity of the described spectrometer is 75 parts per million. Applications of this technology include the detection of polluting or toxic gases, biomedical sensing, atmospheric research, volcanic monitoring and industrial process control.