Schedule path optimization for quantum annealing and adiabatic quantum computing

Adiabatic quantum computing and optimization have garnered much attention recently as possible models for achieving a quantum advantage over classical approaches to optimization and other special purpose computations. Both techniques are probabilistic in nature and the minimum gap between the ground state and first excited state of the system during evolution is a major factor in determining the success probability. In this work we investigate a strategy for increasing the minimum gap and success probability by introducing intermediate Hamiltonians that modify the evolution path between initial and final Hamiltonians. We focus on an optimization problem relevant to recent hardware implementations and present numerical evidence for the existence of a purely local intermediate Hamiltonian that achieve the optimum performance in terms of pushing the minimum gap to one of the end points of the evolution. As a part of this study we develop a convex optimization formulation of the search for optimal adiabatic schedules that makes this computation more tractable, and which may be of independent interest. We further study the effectiveness of random intermediate Hamiltonians on the minimum gap and success probability, and empirically find that random Hamiltonians have a significant probability of increasing the success probability, but only by a modest amount.Comment: ~10 page

Large fine‐scale spatiotemporal variations of CH4 diffusive fluxes from shrimp aquaculture ponds affected by organic matter supply and aeration in Southeast China

Mariculture shrimp ponds are important CH4 sources to the atmosphere. However, the spatiotemporal variations of CH4 concentration and flux at fine spatial scales in mariculture ponds are poorly known, particularly in China, worlds largest aquaculture producer. In this study, the plot‐scale spatiotemporal variations of water CH4 concentration and flux, both within and among ponds, were researched in shrimp ponds in Shanyutan wetland, Min River Estuary, Southeast China. The average water CH4 concentration and diffusion flux across the water‐air interface in the shrimp ponds over the shrimp aquaculture period varied from 2.29 ± 0.29 to 50.48 ± 20.91 μM and from 0.09 ± 0.01 to 2.32 ± 0.95 mmol·m−2·hr−1, respectively. The CH4 emissions from the estuarine ponds varied greatly between seasons, with peaks in August and September, which was similar to the trend of water temperature and dissolved oxygen concentrations. There was no remarkable difference in CH4 concentration and flux between shrimp ponds but significantly spatiotemporal differences in CH4 concentration and flux within the ponds. Significantly higher emissions occurred in the feeding zone, accounting for approximately 60% of total CH4 emission flux, while much lower CH4 emissions appeared in aeration zone, contributing 14% to total flux. This study suggests the importance of considering spatiotemporal variation in the whole‐pond estimates of CH4 concentration and flux. In light of such high spatial variation within ponds, improving aeration and feed utilization efficiency would help to mitigate CH4 emissions from mariculture ponds

Adaptive growth of Tamarix taklamakanensis root systems in response to wind action

Root distribution and characteristics were investigated on a 70-year-old Tamarix taklamakanensis individual through uprooting. Rooting depth was restricted by water table, and root morphology adapted to resist the wind movement associated with shallow rooting. Root systems had more structural root mass and length on the leeward side than the windward side of the tree relative to the prevailing wind direction. Additional resistance to wind bending can occur as a result of increased thickening of the lower stem along the axis of the prevailing wind direction, and in T taklamakanensis, this thickening is greater on the lee side of the stem. We conclude that increased root distribution and thickening of the lower stem on the leeward are an important strategy for T taklamakanensis in response to wind action in the hinterland of Taklimakan Desert

Plants water status of the shelterbelt along the Tarim Desert Highway

The plant water consumption and irrigation management are the core issue of the sustainable growing of the Tarim Desert Highway shelterbelt in the hyperaride Taklimakan Desert. The stem sap flow, water status and water consumption of shelterbelt plants were studied, then, the issue of the water save in the process of shelterbelt irrigation management was discussed by measuring the sap flow of shelterbelt plants with a stem sap flow gauge. The stem sap flow exhibited a distinct diurnal course with maximum values between 10:00 and 15:00, and minimum values between 00:00 and 03:00. Generally, sap flow was lower at night than during the day. The daily average stem sap flow of Calligonum arborescens, Tamarix ramosissima and Haloxylon ammodendron (diameter 1.9-2.0 cm) was 67.2 g.h(-1), 77.05 g.h(-1) and 61.54 g.h(-1) respectively. The sap flow was influenced by environmental factors, and the solar radiation, wind velocity, temperature and relative humidity were significantly correlative with plant stem sap flow. The annual water consumption of 8-a Calligonum arborescens, Tamarix ramosissima and Haloxylon ammodendron was 1937.80 kg, 1253.39 kg and 1026.96 kg, while daily average water consumption was 9.69 kg, 6.27 kg and 5.13 kg respectively. Under drip irrigation, soil moisture content of the shelterbelt in different months indicated no obvious fluctuation, and soil moisture was adequate. The predawn and midday plant water potential reflected that the plant water status was in good conditions. There is still some water-saving space if optimizing the present water management, integrating water resources conservation and protection performance

Positive solutions of higher order fractional integral boundary value problem with a parameter

In this paper, we study a higher-order fractional differential equation with integral boundary conditions and a parameter. Under different conditions of nonlinearity, existence and nonexistence results for positive solutions are derived in terms of different intervals of parameter. Our approach relies on the Guo–Krasnoselskii fixed point theorem on cones

Does a Distributed Practice Strategy for Multiple Choice Questions Help Novices Learn Programming?

Learning how to program is becoming essential in many disciplines. However, programming cannot be easily learned, especially by non-engineering students. It is challenging to conduct engineering education for non-engineering majored students. Therefore, it is important to teach non-engineering students to learn with efficient learning strategies. To discover an efficient learning strategy, we had 64 students practice programming with a simple learning management system and tracked all of their practice behaviors on multiple choice questions. The learning management system assigned one multiple choice question per day, but let students themselves decide their own practice frequencies. Students could also make unsynchronized communications by commenting on the questions. By analyzing their behavior patterns and other performance indicators, this paper compared the effect of two different practice strategies for multiple choice questions: distributed practice and massed practice. Our analysis found that students who adopted distributed practice significantly outperformed those who adopted massed practice on final exams (p=0.031). We further explored the possible reasons that led to this significant difference. Students who adopted distributed practice strategy tended to make higher percentage of first submission correctness, be more cautious while correcting errors, and be more constructive in posting question-related comments

Existence and Uniqueness of Solution to Nonlinear Boundary Value Problems with Sign-Changing Green’s Function

By using the cone theory and the Banach contraction mapping principle, the existence and uniqueness results are established for nonlinear higher-order differential equation boundary value problems with sign-changing Green’s function.The theorems obtained are very general and complement previous known results

Multiple solutions for a modified quasilinear Schrödinger elliptic equation with a nonsquare diffusion term

In this paper, we establish the results of multiple solutions for a class of modified nonlinear Schrödinger equation involving the p-Laplacian. The main tools used for analysis are the critical points theorems by Ricceri and the dual approach

Toward a Better Estimation of Functional Brain Network for Mild Cognitive Impairment Identification: A Transfer Learning View

Mild cognitive impairment (MCI) is an intermediate stage of brain cognitive decline, associated with increasing risk of developing Alzheimer's disease (AD). It is believed that early treatment of MCI could slow down the progression of AD, and functional brain network (FBN) could provide potential imaging biomarkers for MCI diagnosis and response to treatment. However, there are still some challenges to estimate a "good" FBN, particularly due to the poor quality and limited quantity of functional magnetic resonance imaging (fMRI) data from the target domain (i.e., MCI study). Inspired by the idea of transfer learning, we attempt to transfer information in high-quality data from source domain (e.g., human connectome project in this paper) into the target domain towards a better FBN estimation, and propose a novel method, namely NERTL (Network Estimation via Regularized Transfer Learning). Specifically, we first construct a high-quality network "template" based on the source data, and then use the template to guide or constrain the target of FBN estimation by a weighted l1-norm regularizer. Finally, we conduct experiments to identify subjects with MCI from normal controls (NCs) based on the estimated FBNs. Despite its simplicity, our proposed method is more effective than the baseline methods in modeling discriminative FBNs, as demonstrated by the superior MCI classification accuracy of 82.4% and the area under curve (AUC) of 0.910

A sufficient and necessary condition of existence of blow-up radial solutions for a k-Hessian equation with a nonlinear operator

In this paper, we establish the results of nonexistence and existence of blow-up radial solutions for a k-Hessian equation with a nonlinear operator. Under some suitable growth conditions for nonlinearity, the result of nonexistence of blow-up solutions is established, a sufficient and necessary condition on existence of blow-up solutions is given, and some further results are obtained.&nbsp