Market Stability Switches in a Continuous-Time Financial Market with Heterogeneous Beliefs

By considering a financial market of fundamentalists and trend followers in which the price trend of the trend followers is formed as a weighted average of historical prices, we establish a continuous-time financial market model with time delay and examines the impact of time delay on market price dynamics. Conditions for the stability of the fundamental price in terms of agents' behavior parameters and time delay are obtained. In particular, it is found that an increase in time delay can not only destabilize the market price but also stabilize an otherwise unstable market price, leading to stability switching as delay increases. This interesting phenomena shed new light in understanding of mechanism on the market stability. When the fundamental price becomes unstable through Hopf bifurcations, suffcient conditions on the stability and global existence of the periodic solution are obtained.asset price; fundamentalists; trend followers; delay differential equations; stability; bifurcations

Drosophila Spastin Regulates Synaptic Microtubule Networks and Is Required for Normal Motor Function

Nina Tang Sherwood is with California Institute of Technology, Qi Sun is with California Institute of Technology, Mingshan Xue is with UT Austin, Bing Zhang is with UT Austin, Kai Zinn is with California Institute of Technology.The most common form of human autosomal dominant hereditary spastic paraplegia (AD-HSP) is caused by mutations in the SPG4 (spastin) gene, which encodes an AAA ATPase closely related in sequence to the microtubule-severing protein Katanin. Patients with AD-HSP exhibit degeneration of the distal regions of the longest axons in the spinal cord. Loss-of-function mutations in the Drosophila spastin gene produce larval neuromuscular junction (NMJ) phenotypes. NMJ synaptic boutons in spastin mutants are more numerous and more clustered than in wild-type, and transmitter release is impaired. spastin-null adult flies have severe movement defects. They do not fly or jump, they climb poorly, and they have short lifespans. spastin hypomorphs have weaker behavioral phenotypes. Overexpression of Spastin erases the muscle microtubule network. This gain-of-function phenotype is consistent with the hypothesis that Spastin has microtubule-severing activity, and implies that spastin loss-of-function mutants should have an increased number of microtubules. Surprisingly, however, we observed the opposite phenotype: in spastin-null mutants, there are fewer microtubule bundles within the NMJ, especially in its distal boutons. The Drosophila NMJ is a glutamatergic synapse that resembles excitatory synapses in the mammalian spinal cord, so the reduction of organized presynaptic microtubules that we observe in spastin mutants may be relevant to an understanding of human Spastin's role in maintenance of axon terminals in the spinal cord.Biological Sciences, School o

Multistaged discharge constructing heterostructure with enhanced solid-solution behavior for long-life lithium-oxygen batteries.

Inferior charge transport in insulating and bulk discharge products is one of the main factors resulting in poor cycling stability of lithium-oxygen batteries with high overpotential and large capacity decay. Here we report a two-step oxygen reduction approach by pre-depositing a potassium carbonate layer on the cathode surface in a potassium-oxygen battery to direct the growth of defective film-like discharge products in the successive cycling of lithium-oxygen batteries. The formation of defective film with improved charge transport and large contact area with a catalyst plays a critical role in the facile decomposition of discharge products and the sustained stability of the battery. Multistaged discharge constructing lithium peroxide-based heterostructure with band discontinuities and a relatively low lithium diffusion barrier may be responsible for the growth of defective film-like discharge products. This strategy offers a promising route for future development of cathode catalysts that can be used to extend the cycling life of lithium-oxygen batteries

Deep Item-based Collaborative Filtering for Top-N Recommendation

Item-based Collaborative Filtering(short for ICF) has been widely adopted in recommender systems in industry, owing to its strength in user interest modeling and ease in online personalization. By constructing a user's profile with the items that the user has consumed, ICF recommends items that are similar to the user's profile. With the prevalence of machine learning in recent years, significant processes have been made for ICF by learning item similarity (or representation) from data. Nevertheless, we argue that most existing works have only considered linear and shallow relationship between items, which are insufficient to capture the complicated decision-making process of users. In this work, we propose a more expressive ICF solution by accounting for the nonlinear and higher-order relationship among items. Going beyond modeling only the second-order interaction (e.g. similarity) between two items, we additionally consider the interaction among all interacted item pairs by using nonlinear neural networks. Through this way, we can effectively model the higher-order relationship among items, capturing more complicated effects in user decision-making. For example, it can differentiate which historical itemsets in a user's profile are more important in affecting the user to make a purchase decision on an item. We treat this solution as a deep variant of ICF, thus term it as DeepICF. To justify our proposal, we perform empirical studies on two public datasets from MovieLens and Pinterest. Extensive experiments verify the highly positive effect of higher-order item interaction modeling with nonlinear neural networks. Moreover, we demonstrate that by more fine-grained second-order interaction modeling with attention network, the performance of our DeepICF method can be further improved.Comment: 25 pages, submitted to TOI

Synthesis and structures of O-anthrylmethyl-substituted hexahomotrioxacalix[3]arenes

O-Alkylation of 7,15,23-tri-tert-butyl-25,26,27-trihydroxy-2,3,10,11,18,19-hexahomo-3,11,19-trioxacalix[3]arene (1H₃) with 9-chloromethylanthracene 5 was carried out under different reaction conditions. Variation of the number of anthrylmethyl group introduced at the phenolic rim of hexahomotrioxacalix[3]arene 1H₃ was achieved through selective O-alkylation using stoichiometric amounts of 9-chloromethylanthracene 5 in acetone to afford the mono-O-alkylated product 2H₂An, the di-O-alkylated product 3HAn₂ and the tri-O-alkylated product partial-cone-4An₃, respectively. Interestingly, by using an acetone/benzene (1:1 v/v) mixed solvent system, the cone-4An₃ was successfully synthesized. These results suggest that the solvent can also control the conformation of the O-alkylation products. The possible reaction routes of the cone-4An₃ and partial-cone-4An₃ are also discussed