A convex code is a binary code generated by the pattern of intersections of a collection of open convex sets in some Euclidean space. Convex codes are relevant to neuroscience as they arise from the activity of neurons that have convex receptive fields. In this paper, we develop algebraic methods to determine if a code is convex. Specifically, we use the neural ideal of a code, which is a generalization of the Stanley–Reisner ideal. Using the neural ideal together with its standard generating set, the canonical form, we provide algebraic signatures of certain families of codes that are non-convex. We connect these signatures to the precise conditions on the arrangement of sets that prevent the codes from being convex. Finally, we also provide algebraic signatures for some families of codes that are convex, including the class of intersection-complete codes. These results allow us to detect convexity and non-convexity in a variety of situations, and point to some interesting open questions. 相似文献
Transient dynamics of allophycocyanin trimers and monomers are observed by using the pump-probe, transient absorption technique.
The origin of spectral components of the transient absorption spectra is discussed in terms of both kinetics and spectroscopy.
We find that the energy gap between the ground and excited states of the unexcited subunit of allophycocyanin monomer decreases
via an interaction with another excited subunit. For allophycocyanin trimer, we find that the fast dynamics results from the
fast internal conversion and the first excited state is the only one electronic state which can trap the final population. 相似文献
Heating of [Ir(η2-ppy)2(MeCN)2]NO3 (1, ppy = 2-phenylpyridine) in MeCN under reflux afforded [Ir(η2-ppy)2(η2-NO3)] (2). Treatment of 1 with 2-mercaptopyridine (Hmp), 6-methyl-2-hydroxypyridine (Hmhp), 6-chloro-2-hydroxypyridine (Hchp), trimethylacetic acid (Htma), benzoic acid (Hbz), 2-methylacrylic acid (Hma), and acetic acid (Hac) in the presence of excess Et3N produced [Ir(η2-ppy)2(η2-XZY)] (XZY? = mp? (3), mhp? (4), chp? (5), ac? (6), bz? (7), ma? (8), tma? (9)). Crystal structures of 2, 3, 7, 8, and 9 have been characterized by X-ray diffraction. The inherent strain contained in the four-member rings, {Ir(η2-XZY)}, is apparently reflected in the long Ir–X and Ir–Y distances. The absorption and emission properties of nearly all the new complexes except 2 show small variations. 相似文献
Gel electrophoresis and capillary gel electrophoresis are widely used for the separation of biomolecules. With increasing demand in the miniaturized devices such as lab-on-a-chip, it is necessary to integrate such a separation component into a chip format. Here, we describe a simple approach to fabricate robust three-dimensional periodic porous nanostructures inside the microchannels for the separation of DNA molecules. In our approach, the colloidal crystals were first grown inside the microchannel using evaporation assisted self-assembly process. Then the void spaces among the colloidal crystals were filled with epoxy-based negative tone photoresist (SU-8). UV radiation was used to cure the photoresist at the desired area inside the microchannel. After subsequent development and nanoparticle removal, the well-ordered nanoporous structures inside the microchannel were obtained. Our results indicated that it was possible to construct periodic porous nanostructures inside the microchannels with cavity size around 300 nm and interconnecting pores around 30 nm. The mobility of large DNA molecules with different sizes was measured as a function of the applied electric field in the nanoporous materials. It was also demonstrated that 1 kilo-base pair (kbp) DNA ladders could be separated in such an integrated system within 10 min under moderate electric field. 相似文献
A molecular theory of time-resolved sum-frequency generation (SFG) has been developed. The theoretical framework is constructed using the coupled-oscillator model in the adiabatic approximation. This theory can treat not only the vibrational spectroscopy but also vibrational dynamics. An application of this theory is also provided for estimation of the time constants of the intermolecular vibrational energy transfer between water molecules. This approach can be used for molecular analysis of the experimental results of Shen at al. on the SFG studies of vibrational dynamics of water. 相似文献
Two luminescent, monoanionic chalcogenide-centered nonanuclear silver clusters stabilized by dichalcogenophosphates were synthesized and fully characterized by various spectroscopies including multinuclear NMR and ESI-mass. Single crystal X-ray diffraction studies on both cluster anions, [Ag9(S){S2P(OEt)2}8]?, 1, and [Ag9(Se){Se2P(OEt)2}8]?, 2, reveal that the nine silver atoms form an extremely distorted tricapped trigonal prism, which has an encapsulating chalcogenide. The coordination geometry of the central chalcogenide appears to be monocapped trigonal prismatic, which was analyzed by DFT calculations. The origin of the yellow emission is assigned by TDDFT calculations to originate from a chalcogen (ligand + encapsulated) → silver charge transfer. 相似文献
Metal ions are prevalent in biological systems and are critically involved in essential life processes. However, excess concentrations of metals can pose a serious danger to living organisms. Oligonucleotides represent a versatile sensing platform for the detection of various molecular entities including metal ions. This review summarizes the recent advances in the development of oligonucleotide‐based luminescent detection methods for metal ions. 相似文献
We throw i.i.d. random squares S1,S2,… with respective side lengths l1,l2,… uniformly on the two-dimensional torus ?/?×?/?, where $\{l_{n}\}_{n=1}^{\infty}$ is a nonincreasing sequence with 0<ln<1 and limn→∞ln=0. A necessary and sufficient condition for covering the connected curve {0}×?/? is $$\sum_{n=1}^{\infty}\frac{l_n}{(\sum_{i=1}^{n}l_i)^2}\exp{\Biggl(\sum _{i=1}^{n}l_i^2\Biggr)}=\infty.$$相似文献
Enriched cleavage : An efficient chemoselective cysteine modification of unprotected peptides and proteins has been developed by using electron‐deficient alkynes in aqueous media. Interestingly, terminal alkynone‐modified peptides could be converted back into the unmodified peptides by cleavage by adding thiols under mild conditions (see scheme).