MARS: A second-order reduction algorithm for high-dimensional sparse precision matrices estimation

Estimation of the precision matrix (or inverse covariance matrix) is of great importance in statistical data analysis. However, as the number of parameters scales quadratically with the dimension p, computation becomes very challenging when p is large. In this paper, we propose an adaptive sieving reduction algorithm to generate a solution path for the estimation of precision matrices under the $\ell_1$ penalized D-trace loss, with each subproblem being solved by a second-order algorithm. In each iteration of our algorithm, we are able to greatly reduce the number of variables in the problem based on the Karush-Kuhn-Tucker (KKT) conditions and the sparse structure of the estimated precision matrix in the previous iteration. As a result, our algorithm is capable of handling datasets with very high dimensions that may go beyond the capacity of the existing methods. Moreover, for the sub-problem in each iteration, other than solving the primal problem directly, we develop a semismooth Newton augmented Lagrangian algorithm with global linear convergence on the dual problem to improve the efficiency. Theoretical properties of our proposed algorithm have been established. In particular, we show that the convergence rate of our algorithm is asymptotically superlinear. The high efficiency and promising performance of our algorithm are illustrated via extensive simulation studies and real data applications, with comparison to several state-of-the-art solvers

An efficient sieving based secant method for sparse optimization problems with least-squares constraints

In this paper, we propose an efficient sieving based secant method to address the computational challenges of solving sparse optimization problems with least-squares constraints. A level-set method has been introduced in [X. Li, D.F. Sun, and K.-C. Toh, SIAM J. Optim., 28 (2018), pp. 1842--1866] that solves these problems by using the bisection method to find a root of a univariate nonsmooth equation $\varphi(\lambda) = \varrho$ for some $\varrho > 0$, where $\varphi(\cdot)$ is the value function computed by a solution of the corresponding regularized least-squares optimization problem. When the objective function in the constrained problem is a polyhedral gauge function, we prove that (i) for any positive integer $k$, $\varphi(\cdot)$ is piecewise $C^k$ in an open interval containing the solution $\lambda^*$ to the equation $\varphi(\lambda) = \varrho$; (ii) the Clarke Jacobian of $\varphi(\cdot)$ is always positive. These results allow us to establish the essential ingredients of the fast convergence rates of the secant method. Moreover, an adaptive sieving technique is incorporated into the secant method to effectively reduce the dimension of the level-set subproblems for computing the value of $\varphi(\cdot)$. The high efficiency of the proposed algorithm is demonstrated by extensive numerical results

Model-based Optimal Control of Variable Air Volume Terminal Box

In the U.S. A Variable Air Volume (VAV) system is one of most commonly used air system for multiple-zone commercial buildings due to its capability to meet the varying heating and cooling loads of different building thermal zones. One of key component of VAV system is the terminal VAV box. There are an air damper and a reheat coil in the box. How to effectively and efficiently control the VAV box plays a significant role to reduce energy consumption and maintain acceptable indoor environment in buildings. Currently, there are two control logics used for controlling VAV box, namely, single maximum and dual maximum control logics. The single maximum logic is the most common, where the room temperature setpoint is maintained by only adjusting the reheat coil valve position in the heating model. The damper position is kept as the minimal to satisfy the ventilation requirement only. On the other hand, the more advanced dual maximum control logic realizes the room air temperature control by adjusting both damper position and reheat coil valve position in the heating model. For the cooling model, both control logics have the same action to maintain room air temperature setpoint through adjusting the damper position. Â In this study, a model-based optimal control is explored to minimize the energy consumption of the VAV box with a hot water reheat coil. Data driven approach based on an Autoregressive exogenous (ARX) model is investigated to represent dynamics of the room thermal response. The similar data-driven approach is used to develop an energy consumption model of the VAV box. Measured data for the VAV box from a real building is used to train and test data-driven model. Such data includes room air temperature, outdoor air temperature, supply air temperature, supply air flow rate, damper position, reheat coil valve position and VAV box energy consumption. A platform of AMPL (A Modeling Language for Mathematical Programming) is used to for mathematical modeling and links to different optimization solvers. Â In addition, uncertainty analysis and sensitivity analysis are conducted to help understand the model behaviors and performance. In this study, the Monte Carlo sampling method is applied to generate samples for model inputs including supply air temperature, outdoor conditions, etc. A quantified sensitivity index of Sobol is calculated to indicate the impact level from different inputs or disturbances

Investigation on A Ground Source Heat Pump System Integrated With Renewable Sources

Buildings consumed 40% of the energy and represented 40% of the carbon emissions in the United States. This is more than any other sector of the U.S. economy, including transportation and industry. About 24% of all energy used in the nation is for space heating, cooling and water heating in buildings. Enhancing building efficiency represents one of the easiest, most immediate and most cost effective ways to reduce carbon emissions. One of energy efficient and environment friendly technologies with potentials for savings is Ground Source Heat Pump (GSHP) system. On the other hand, solar energy is considered as an unlimited and an environment friendly energy source, which has been widely used for solar thermal and solar power applications. This paper presents a laboratory test facility for a solar powered ground source heat pump system. The ultimate technical goal is to apply the solar powered ground source heat pump into a net-zero energy building, where all the electricity consumption will be covered by an integrated on-site solar Photovoltaics (PV) panels and battery system. The added-on benefits from this solar powered GSHP include but not limited to: 1) help further reduce electricity peak demand and 2) help further reduce greenhouse emissions. In this test rig, a ¾ - ton water-to-air GSHP is connected to two 60-feet deep wells. A group of solar PV panels of 1.12KW is connected to a battery bank, which is used to power the GSHP and a 0.27KW DC powered well pump. During the daytime, solar PV panels convert solar photons into electrical energy which will be stored into the battery bank. Whenever the GSHP system is on demand, the battery bank will provide the power. This test rig also has a comprehensive performance monitoring and data acquisition system. Well groundwater temperatures, refrigerant temperatures, air temperatures, water flow rates, etc. are all real-time monitored, trended and stored. In addition, an on-site weather station is installed to measure outside air temperature, relative humidity, wind speed and direction, and solar radiation. The details for the design and layout of this solar powered GSHP, together with the monitoring and data acquisition system will be introduced in this paper. In addition, the preliminary data collected from a testing of a cooling mode operation will be presented to illustrate the benefits of the proposed system. Finally, the feasibility of the application of the system will be discussed in the paper

Topological and metrical property characterization of radical subunits for ternary hard sphere crystals

Quantitative characterization on the topological and metrical properties of radical subunits (polyhedra) for two new ternary hard sphere crystals was studied. These two ideal crystalline structures are numerically constructed by filling small and medium spheres into interstices (corresponding to regular tetrahedral and octahedral pores) of perfect face centered cubic (FCC) and hexagonal close packed (HCP) crystals formed by the packing of large spheres. Topological properties such as face number, edge number, vertex number of each radical polyhedron (RP), edge number of each RP face and metrical properties such as volume, surface area, total perimeter and pore volume of each RP, area and perimeter of each RP face were analyzed and compared. The results show that even though the overall packing densities for FCC and HCP ternary crystals are the same, different characteristics of radical polyhedra for corresponding spheres in these two crystals can be identified. That is, in the former structure RPs are more symmetric than those in the latter; the orientations of corresponding RP in the latter are twice as many as that in the former. Moreover, RP topological and metrical properties in the HCP ternary crystal are much more complicated than those in the FCC ternary crystal. These differences imply the structure and property differences of these two ternary crystals. Analyses of RPs provide intensive understanding of pores in the structure

Impact of Ferrous Iron on Microbial Community of the Biofilm in Microbial Fuel Cells

The performance of microbial electrochemical cells depends upon microbial community structure and metabolic activity of the electrode biofilms. Iron as a signal affects biofilm development and enrichment of exoelectrogenic bacteria. In this study, the effect of ferrous iron on microbial communities of the electrode biofilms in microbial fuel cells (MFCs) was investigated. Voltage production showed that ferrous iron of 100 μM facilitated MFC start-up compared to 150 μM, 200 μM, and without supplement of ferrous iron. However, higher concentration of ferrous iron had an inhibitive influence on current generation after 30 days of operation. Illumina Hiseq sequencing of 16S rRNA gene amplicons indicated that ferrous iron substantially changed microbial community structures of both anode and cathode biofilms. Principal component analysis showed that the response of microbial communities of the anode biofilms to higher concentration of ferrous iron was more sensitive. The majority of predominant populations of the anode biofilms in MFCs belonged to Geobacter, which was different from the populations of the cathode biofilms. An obvious shift of community structures of the cathode biofilms occurred after ferrous iron addition. This study implied that ferrous iron influenced the power output and microbial community of MFCs

Numerical Analysis of Resistance Characteristics of a Novel High-Speed Quadramaran

This paper utilised computational fluid dynamics (CFD) technology to calculate the resistance of a novel high-speed quadramaran in calm water using the Navier‒Stokes (N‒S) equation, analysed the total resistance, frictional resistance, and residual resistance characteristics of this novel high-speed quadramaran at different length Froude numbers, and compared them with the results of a conventional high-speed catamaran with the same displacement. The results showed that the total resistance of the quadramaran had a significant hump at the Froude number of 0.6, due to the complexity of the wave interference among the four demihulls, and the hump value was about 1.6 times that of the catamaran. Above the hump speed, the total resistance of the quadramaran decreased with the increase of the Froude number, until reaching the Froude number of 1.06, when the curve became flat, and it showed a maximum resistance reduction of 40% at the Froude number of 1.66 compared with the catamaran, where the total resistance curve was steep. The frictional resistance of the quadramaran increased gradually with the growth of the Froude number, which was basically consistent with the change trend of the catamaran. The residual resistance of the quadramaran first rose and then reduced with the rising Froude number, the curve showed a large hump due to the adverse wave interference, and the hump value was about 1.7 times that of the catamaran. Above the Froude number of 1.06, as the wave interference changed from adverse to favourable, the quadramaran had lower residual resistance than the catamaran. The bow and stern demihulls of the quadramaran were also analysed for their resistance characteristics. The total resistance of the bow demihulls increased gradually with the increase of the Froude number, the curve had a small hump at the Froude number of 0.7, and above the hump speed, the curve was steep. The total resistance of the stern demihulls first increased and then decreased with the growth of the Froude number, the hump value at the Froude number of 0.85 was significant and was about 2 times that of the bow demihulls, and the curve became flat above the Froude number of 1.51

Peptidase inhibitor 15 as a novel blood diagnostic marker for cholangiocarcinomaResearch in context

Background: We aimed to screen a specific secretory protein that could serve as blood diagnostic marker for cholangiocarcinoma (CCA). Methods: Starting with the analysis of gene expression profiles in tumor tissues and matched normal tissues from cases with CCA and hepatocellular carcinoma (HCC), we identified peptidase inhibitor 15 (PI15) was a potential diagnostic marker for CCA. We demonstrated PI15 expression levels in CCA, HCC, and normal liver tissues. Furthermore, quantitative enzyme-linked immunosorbent assay (ELISA) assessed plasma PI15 levels in CCA (n = 61), HCC (n = 72), benign liver disease (n = 28), chronic hepatitis B (CHB) patients (n = 45), and healthy individuals (n = 45). The diagnostic value of PI15 was estimated by the area under the receiver operating characteristic (ROC) curve (AUC). Findings: The positive rate of PI15 expression was 70% in CCA and only 9.1% in HCC; PI15 was not detected in normal liver tissue. High levels of plasma PI15 were evident in CCA patients, whereas only low levels were observed in cases involving HCC, benign liver disease, CHB patients, and healthy individuals. Plasma PI15 levels in CCA patients were obviously reduced (p = .0014) after surgery. The AUC of plasma PI15 for discriminating between CCA and HCC was 0.735. Furthermore, with a specificity of 94.44%, the combination of CA19–9 (>98.5 U/ml) and PI15 (>13 ng/ml) yielded a sensitivity of 80.39% for CCA and HCC. Interpretation: PI15 exhibits promise as a novel marker for predicting the diagnosis and follow-up of CCA patients. Fund: Natural Science Research Foundation of Anhui Province and Natural Science Foundation of China Keywords: Cholangiocarcinoma, PI15, Biomarker, Blood diagnosi

MOESM1 of Multiple syntrophic interactions drive biohythane production from waste sludge in microbial electrolysis cells

Additional file 1: Table. S1. Similarity-based OTUs and species richness and diversity estimates of bacteria in different systems. Figure. S1. Current density of MEC fed with raw sludge (RS-MEC) and alkali-pretreated waste sludge (AS-MEC). Figure. S2. Variations of SCOD (A), soluble protein (B) and carbohydrates concentration (C) of raw sludge open-circuit MEC (RS-OCMEC), MEC fed with raw sludge (RS-MEC) or alkali-pretreated sludge (AS-MEC)