The Abel-Zeilberger Algorithm

We use both Abel's lemma on summation by parts and Zeilberger's algorithm to find recurrence relations for definite summations. The role of Abel's lemma can be extended to the case of linear difference operators with polynomial coefficients. This approach can be used to verify and discover identities involving harmonic numbers and derangement numbers. As examples, we use the Abel-Zeilberger algorithm to prove the Paule-Schneider identities, the Apery-Schmidt-Strehl identity, Calkin's identity and some identities involving Fibonacci numbers.Comment: 18 page

Thermal tunability in terahertz metamaterials fabricated on strontium titanate single crystal substrates

We report an experimental demonstration of thermal tuning of resonance frequency in a planar terahertz metamaterial consisting of a gold split-ring resonator array fabricated on a bulk single crystal strontium titanate (SrTiO3) substrate. Cooling the metamaterial starting from 409 K down to 150 K causes about 50% shift in resonance frequency as compare to its room temperature resonance, and there is very little variation in resonance strength. The resonance shift is due to the temperature-dependent refractive index (or the dielectric constant) of the strontium titanate. The experiment opens up avenues for designing tunable terahertz devices by exploiting the temperature sensitive characteristic of high dielectric constant substrates and complex metal oxide materials.Comment: 6 pages, 3 figures, accepted at Optics Letter

Energy Efficient Power Allocation for OFDM-Based Cognitive Radio Systems with Partial Intersystem CSI

This paper investigates energy efficient power allocation for orthogonal frequency division multiplexing- (OFDM-) based cognitive radio (CR) systems with partial intersystem channel state information (CSI) available. The goal is to maximize energy efficiency (EE) while ensuring the minimum rate of secondary user (SU) and keeping the average interference power (AIP) introduced to primary user (PU) within a target probability level. We propose a suboptimal algorithm to solve this optimization problem based on classic water-filling (WF) technique. Moreover, we first address the relation between EE and water level. In order to reduce complexity, a simplified algorithm with closed-form solution is also proposed. Numerical results are provided to corroborate our theoretical analysis and to demonstrate the effectiveness of the proposed schemes

A role of corazonin receptor in larval-pupal transition and pupariation in the oriental fruit fly Bactrocera dorsalis (Hendel) (Diptera: Tephritidae)

Corazonin (Crz) is a neuropeptide hormone, but also a neuropeptide modulator that is internally released within the CNS, and it has a widespread distribution in insects with diverse physiological functions. Here, we identified and cloned the cDNAs of Bactrocera dorsalis that encode Crz and its receptor CrzR. Mature BdCrz has 11 residues with a unique Ser11 substitution (instead of the typical Asn) and a His in the evolutionary variable position 7. The BdCrzR cDNA encodes a putative protein of 608 amino acids with 7 putative transmembrane domains, typical for the structure of G-protein-coupled receptors. When expressed in Chinese hamster ovary (CHO) cells, the BdCrzR exhibited a high sensitivity and selectivity for Crz (EC50 approximate to 52.5 nM). With qPCR, the developmental stage and tissue-specific expression profiles in B. dorsalis demonstrated that both BdCrz and BdCrzR were highly expressed in the larval stage, and BdCrzR peaked in 2-day-old 3rd-instar larvae, suggesting that the BdCrzR may play an important role in the larval-pupal transition behavior. Immunochemical localization confirmed the production of Crz in the central nervous system (CNS), specifically by a group of three neurons in the dorso-lateral protocerebrum and eight pairs of lateral neurons in the ventral nerve cord. qPCR analysis located the BdCrzR in both the CNS and epitracheal gland, containing the Inka cells. Importantly, dsRNA-BdCrzR-mediated gene-silencing caused a delay in larval-pupal transition and pupariation, and this phenomenon agreed with a delayed expression of tyrosine hydroxylase and dopa-decarboxylase genes. We speculate that CrzR-silencing blocked dopamine synthesis, resulting in the inhibition of pupariation and cuticular melanization. Finally, injection of Crz in head-ligated larvae could rescue the effects. These findings provide a new insight into the roles of Crz signaling pathway components in B. dorsalis and support an important role of CrzR in larval-pupal transition and pupariation behavior

Review of reactive power dispatch strategies for loss minimization in a DFIG-based wind farm

This paper reviews and compares the performance of reactive power dispatch strategies for the loss minimization of Doubly Fed Induction Generator (DFIG)-based Wind Farms (WFs). Twelve possible combinations of three WF level reactive power dispatch strategies and four Wind Turbine (WT) level reactive power control strategies are investigated. All of the combined strategies are formulated based on the comprehensive loss models of WFs, including the loss models of DFIGs, converters, filters, transformers, and cables of the collection system. Optimization problems are solved by a Modified Particle Swarm Optimization (MPSO) algorithm. The effectiveness of these strategies is evaluated by simulations on a carefully designed WF under a series of cases with different wind speeds and reactive power requirements of the WF. The wind speed at each WT inside the WF is calculated using the Jensen wake model. The results show that the best reactive power dispatch strategy for loss minimization comes when the WF level strategy and WT level control are coordinated and the losses from each device in the WF are considered in the objective

Deep Group Interest Modeling of Full Lifelong User Behaviors for CTR Prediction

Extracting users' interests from their lifelong behavior sequence is crucial for predicting Click-Through Rate (CTR). Most current methods employ a two-stage process for efficiency: they first select historical behaviors related to the candidate item and then deduce the user's interest from this narrowed-down behavior sub-sequence. This two-stage paradigm, though effective, leads to information loss. Solely using users' lifelong click behaviors doesn't provide a complete picture of their interests, leading to suboptimal performance. In our research, we introduce the Deep Group Interest Network (DGIN), an end-to-end method to model the user's entire behavior history. This includes all post-registration actions, such as clicks, cart additions, purchases, and more, providing a nuanced user understanding. We start by grouping the full range of behaviors using a relevant key (like item_id) to enhance efficiency. This process reduces the behavior length significantly, from O(10^4) to O(10^2). To mitigate the potential loss of information due to grouping, we incorporate two categories of group attributes. Within each group, we calculate statistical information on various heterogeneous behaviors (like behavior counts) and employ self-attention mechanisms to highlight unique behavior characteristics (like behavior type). Based on this reorganized behavior data, the user's interests are derived using the Transformer technique. Additionally, we identify a subset of behaviors that share the same item_id with the candidate item from the lifelong behavior sequence. The insights from this subset reveal the user's decision-making process related to the candidate item, improving prediction accuracy. Our comprehensive evaluation, both on industrial and public datasets, validates DGIN's efficacy and efficiency