Monotonicity testing and shortest-path routing on the cube

We study the problem of monotonicity testing over the hypercube. As previously observed in several works, a positive answer to a natural question about routing properties of the hypercube network would imply the existence of efficient monotonicity testers. In particular, if any set of source-sink pairs on the directed hypercube (with all sources and all sinks distinct) can be connected with edge-disjoint paths, then monotonicity of functions $f:\{ 0,1\} ^n \to \mathcal{R}$ can be tested with O(n/∈) queries, for any totally ordered range $\mathcal{R}$ . More generally, if at least a µ(n) fraction of the pairs can always be connected with edge-disjoint paths then the query complexity is O(n/(∈µ(n))). We construct a family of instances of Ω(2 ⁿ ) pairs in n-dimensional hypercubes such that no more than roughly a $\frac{1} {{\sqrt n }}$ fraction of the pairs can be simultaneously connected with edge-disjoint paths. This answers an open question of Lehman and Ron [16], and suggests that the aforementioned appealing combinatorial approach for deriving query-complexity upper bounds from routing properties cannot yield, by itself, query-complexity bounds better than ≈ n ^3/2. Additionally, our construction can also be used to obtain a strong counterexample to Szymanski’s conjecture about routing on the hypercube. In particular, we show that for any δ > 0, the n-dimensional hypercube is not $n^{\tfrac{1} {2} - \delta }$ -realizable with shortest paths, while previously it was only known that hypercubes are not 1-realizable with shortest paths. We also prove a lower bound of Ω(n/∈) queries for one-sided non-adaptive testing of monotonicity over the n-dimensional hypercube, as well as additional bounds for specific classes of functions and testers.     

Lag synchronization and scaling of chaotic attractor in coupled system

We report a design of delay coupling for lag synchronization in two unidirectionally coupled chaotic oscillators. A delay term is introduced in the definition of the coupling to target any desired lag between the driver and the response. The stability of the lag synchronization is ensured by using the Hurwitz matrix stability. We are able to scale up or down the size of a driver attractor at a response system in presence of a lag. This allows compensating the attenuation of the amplitude of a signal during transmission through a delay line. The delay coupling is illustrated with numerical examples of 3D systems, the Hindmarsh-Rose neuron model, the Ro?ssler system, a Sprott system, and a 4D system. We implemented the coupling in electronic circuit to realize any desired lag synchronization in chaotic oscillators and scaling of attractors.     

Helical folding in heterogeneous foldamers without inter-residual backbone hydrogen-bonding

This communication describes a set of hybrid foldamers that do not feature inter-residual, but intra-residual backbone hydrogen-bonding, yet adopt a preferentially folded conformation displaying right-handed helical architecture. Conformational ordering is apparently due to the combined conformational restrictions imposed by the conformationally restricted individual amino acid residues with which the oligomers are made of.     

Attaining record-high magnetic exchange,magnetic anisotropy and blocking barriers in dilanthanofullerenes

While the blocking barrier (U_eff) and blocking temperature (T_B) for “Dysprocenium” SIMs have been increased beyond liquid N₂ temperature, device fabrication of these molecules remains a challenge as low-coordinate Ln³⁺ complexes are very unstable. Encapsulating the lanthanide ion inside a cage such as a fullerene (called endohedral metallofullerene or EMF) opens up a new avenue leading to several Ln@EMF SMMs. The ab initio CASSCF calculations play a pivotal role in identifying target metal ions and suitable cages in this area. Encouraged by our earlier prediction on Ln₂@C₇₉N, which was verified by experiments, here we have undertaken a search to enhance the exchange coupling in this class of molecules beyond the highest reported value. Using DFT and ab initio calculations, we have studied a series of Gd₂@C_2n (30 ≤ 2n ≤ 80), where an antiferromagnetic J_Gd⋯Gd of −43 cm⁻¹ was found for a stable Gd₂@C₃₈-D_3h cage. This extremely large and exceptionally rare 4f⋯4f interaction results from a direct overlap of 4f orbitals due to the confinement effect. In larger cages such as Gd₂@C₆₀ and Gd₂@C₈₀, the formation of two centre-one-electron (2c-1e⁻) Gd–Gd bonds is perceived. This results in a radical formation in the fullerene cage leading to its instability. To avoid this, we have studied heterofullerenes where one of the carbon atoms is replaced by a nitrogen atom. Specifically, we have studied Ln₂@C₅₉N and Ln₂@C₇₉N, where strong delocalisation of the electron yields a mixed valence-like behaviour. This suggests a double-exchange (B) is operational, and CASSCF calculations yield a B value of 434.8 cm⁻¹ and resultant J_Gd–rad of 869.5 cm⁻¹ for the Gd₂@C₅₉N complex. These parameters are found to be two times larger than the world-record J reported for Gd₂@C₇₉N. Further ab initio calculations reveal an unprecedented U_cal of 1183 and 1501 cm⁻¹ for Dy₂@C₅₉N and Tb₂@C₅₉N, respectively. Thus, this study offers strong exchange coupling as criteria for new generation SMMs as the existing idea of enhancing the blocking barrier via crystal field modulation has reached its saturation point.

Using ab initio calculations, we have made some robust predictions towards lanthanofullerene SMMs exhibiting remarkable characteristics.     

Pyrazine Based Type-I Sensitizing Assemblies for Photoreduction of Cu(II) in ‘One-Pot Three-Component’ CuAAC Reaction Under Aerial Conditions

Photosensitizing assemblies of pyrazine derivative PDA have been developed which exhibit a high photostability, ‘lighted’ excited state, balanced redox potential, high transportation potential and activate oxygen via type-I pathway only. These PDA assemblies in combination with Cu(II) ions catalyze the CuAAC reaction via in situ reduction of Cu(II) ions without any reducing or stabilizing agent. The present protocol has wide substrate scope with recyclability of the catalytic system up to six catalytic cycles and is applicable to gram-scale synthesis.     

Selenium Biofortification: Roles,Mechanisms, Responses and Prospects

The trace element selenium (Se) is a crucial element for many living organisms, including soil microorganisms, plants and animals, including humans. Generally, in Nature Se is taken up in the living cells of microorganisms, plants, animals and humans in several inorganic forms such as selenate, selenite, elemental Se and selenide. These forms are converted to organic forms by biological process, mostly as the two selenoamino acids selenocysteine (SeCys) and selenomethionine (SeMet). The biological systems of plants, animals and humans can fix these amino acids into Se-containing proteins by a modest replacement of methionine with SeMet. While the form SeCys is usually present in the active site of enzymes, which is essential for catalytic activity. Within human cells, organic forms of Se are significant for the accurate functioning of the immune and reproductive systems, the thyroid and the brain, and to enzyme activity within cells. Humans ingest Se through plant and animal foods rich in the element. The concentration of Se in foodstuffs depends on the presence of available forms of Se in soils and its uptake and accumulation by plants and herbivorous animals. Therefore, improving the availability of Se to plants is, therefore, a potential pathway to overcoming human Se deficiencies. Among these prospective pathways, the Se-biofortification of plants has already been established as a pioneering approach for producing Se-enriched agricultural products. To achieve this desirable aim of Se-biofortification, molecular breeding and genetic engineering in combination with novel agronomic and edaphic management approaches should be combined. This current review summarizes the roles, responses, prospects and mechanisms of Se in human nutrition. It also elaborates how biofortification is a plausible approach to resolving Se-deficiency in humans and other animals.     

Pion propagation in real time field theory at finite temperature

We describe how the thermal counterpart of a vacuum two-point function may be obtained in the real time formalism in a simple way by using directly the 2×2 matrices that different elements acquire in this formalism. Using this procedure we calculate the analytic (single component) thermal amplitude for the pion pole term in the ensemble average of two axial-vector currents to two loops in chiral perturbation theory. The general expressions obtained for the effective mass and the decay constants of the pion are evaluated in the chiral and the non-relativistic limits. PACS 11.10.Wx; 12.38.Mh; 12.39.Fe     

Nanoisozymes: Crystal‐Facet‐Dependent Enzyme‐Mimetic Activity of V2O5 Nanomaterials

Nanomaterials with enzyme‐like activity (nanozymes) attract significant interest owing to their applications in biomedical research. Particularly, redox nanozymes that exhibit glutathione peroxidase (GPx)‐like activity play important roles in cellular signaling by controlling the hydrogen peroxide (H₂O₂) level. Herein we report, for the first time, that the redox properties and GPx‐like activity of V₂O₅ nanozyme depends not only on the size and morphology, but also on the crystal facets exposed on the surface within the same crystal system of the nanomaterials. These results suggest that the surface of the nanomaterials can be engineered to fine‐tune their redox properties to act as “nanoisozymes” for specific biological applications.