Control of pattern formation by time-delay feedback with global and local contributions

We consider the suppression of spatiotemporal chaos in the complex GinzburgLandau equation by a combined global and local time-delay feedback. Feedback terms are implemented as a control scheme, i.e., they are proportional to the difference between the time-delayed state of the system and its current state. We perform a linear stability analysis of uniform oscillations with respect to space-dependent perturbations and compare with numerical simulations. Similarly, for the fixed-point solution that corresponds to amplitude death in the spatially extended system, a linear stability analysis with respect to space-dependent perturbations is performed and complemented by numerical simulations. © 2010 Elsevier B.V. All rights reserved.

Into the Bends of Time and Musical Forces in Jazz: Group Interaction and Double-time in “My Foolish Heart” as performed by the Bill Evans Trio with Scott LaFaro and Paul Motian.

Into the Bends of Time is a 40-minute work in seven movements for a large chamber orchestra with electronics, utilizing real-time computer-assisted processing of music performed by live musicians. The piece explores various combinations of interactive relationships between players and electronics, ranging from relatively basic processing effects to musical gestures achieved through stages of computer analysis, in which resulting sounds are crafted according to parameters of the incoming musical material. Additionally, some elements of interaction are multi-dimensional, in that they rely on the participation of two or more performers fulfilling distinct roles in the interactive process with the computer in order to generate musical material. Through processes of controlled randomness, several electronic effects induce elements of chance into their realization so that no two performances of this work are exactly alike. The piece gets its name from the notion that real-time computer-assisted processing, in which sound pressure waves are transduced into electrical energy, converted to digital data, artfully modified, converted back into electrical energy and transduced into sound waves, represents a “bending” of time.

The Bill Evans Trio featuring bassist Scott LaFaro and drummer Paul Motian is widely regarded as one of the most important and influential piano trios in the history of jazz, lauded for its unparalleled level of group interaction. Most analyses of Bill Evans’ recordings, however, focus on his playing alone and fail to take group interaction into account. This paper examines one performance in particular, of Victor Young’s “My Foolish Heart” as recorded in a live performance by the Bill Evans Trio in 1961. In Part One, I discuss Steve Larson’s theory of musical forces (expanded by Robert S. Hatten) and its applicability to jazz performance. I examine other recordings of ballads by this same trio in order to draw observations about normative ballad performance practice. I discuss meter and phrase structure and show how the relationship between the two is fixed in a formal structure of repeated choruses. I then develop a model of perpetual motion based on the musical forces inherent in this structure. In Part Two, I offer a full transcription and close analysis of “My Foolish Heart,” showing how elements of group interaction work with and against the musical forces inherent in the model of perpetual motion to achieve an unconventional, dynamic use of double-time. I explore the concept of a unified agential persona and discuss its role in imparting the song’s inherent rhetorical tension to the instrumental musical discourse.

Microbial community composition and bacterioplankton at time series station Helgoland Roads, North Sea

A process of global importance in carbon cycling is the remineralization of algae biomass by heterotrophic bacteria, most notably during massive marine algae blooms. Such blooms can trigger secondary blooms of planktonic bacteria that consist of swift successions of distinct bacterial clades, most prominently members of the Flavobacteriia, Gammaproteobacteria and the alphaproteobacterial Roseobacter clade. This study explores such successions during spring phytoplankton blooms in the southern North Sea (German Bight) for four consecutive years. The surface water samples were taken at Helgoland Island about 40 km offshore in the southeastern North Sea in the German Bight at the station 'Kabeltonne' (54° 11.3' N, 7° 54.0' E) between the main island and the minor island, Düne (German for 'dune') using small research vessels (http://www.awi.de/en/expedition/ships/more-ships.html). Water depths at this site fluctuate from 6 to 10 m over the tidal cycle. Samples were processed as described previously (Teeling et al., 2012; doi:10.7554/eLife.11888.001) in the laboratory of the Biological Station Helgoland within less than two hours after sampling. Assessment of absolute cell numbers and bacterioplankton community composition was carried out as described previously (Thiele et al., 2011; doi:10.1016/B978-0-444-53199-5.00056-7). To obtain total cell numbers, DNA of formaldehyde fixed cells filtered on 0.2 mm pore sized filters was stained with 4',6-diamidino-2-phenylindole (DAPI). Fluorescently labeled cells were subsequently counted on filter sections using an epifluores-cence microscope. Likewise, bacterioplankton community composition was assessed by catalyzedreporter deposition fluorescence in situ hybridization (CARD-FISH) of formaldehyde fixed cells on 0.2 mm pore sized filters.

Design and implementation of generalized topologies of time-interleaved variable bandpass Σ−Δ modulators

In this thesis, novel analog-to-digital and digital-to-analog generalized time-interleaved variable bandpass sigma-delta modulators are designed, analysed, evaluated and implemented that are suitable for high performance data conversion for a broad-spectrum of applications. These generalized time-interleaved variable bandpass sigma-delta modulators can perform noise-shaping for any centre frequency from DC to Nyquist. The proposed topologies are well-suited for Butterworth, Chebyshev, inverse-Chebyshev and elliptical filters, where designers have the flexibility of specifying the centre frequency, bandwidth as well as the passband and stopband attenuation parameters. The application of the time-interleaving approach, in combination with these bandpass loop-filters, not only overcomes the limitations that are associated with conventional and mid-band resonator-based bandpass sigma-delta modulators, but also offers an elegant means to increase the conversion bandwidth, thereby relaxing the need to use faster or higher-order sigma-delta modulators. A step-by-step design technique has been developed for the design of time-interleaved variable bandpass sigma-delta modulators. Using this technique, an assortment of lower- and higher-order single- and multi-path generalized A/D variable bandpass sigma-delta modulators were designed, evaluated and compared in terms of their signal-to-noise ratios, hardware complexity, stability, tonality and sensitivity for ideal and non-ideal topologies. Extensive behavioural-level simulations verified that one of the proposed topologies not only used fewer coefficients but also exhibited greater robustness to non-idealties. Furthermore, second-, fourth- and sixth-order single- and multi-path digital variable bandpass digital sigma-delta modulators are designed using this technique. The mathematical modelling and evaluation of tones caused by the finite wordlengths of these digital multi-path sigmadelta modulators, when excited by sinusoidal input signals, are also derived from first principles and verified using simulation and experimental results. The fourth-order digital variable-band sigma-delta modulator topologies are implemented in VHDL and synthesized on Xilinx® SpartanTM-3 Development Kit using fixed-point arithmetic. Circuit outputs were taken via RS232 connection provided on the FPGA board and evaluated using MATLAB routines developed by the author. These routines included the decimation process as well. The experiments undertaken by the author further validated the design methodology presented in the work. In addition, a novel tunable and reconfigurable second-order variable bandpass sigma-delta modulator has been designed and evaluated at the behavioural-level. This topology offers a flexible set of choices for designers and can operate either in single- or dual-mode enabling multi-band implementations on a single digital variable bandpass sigma-delta modulator. This work is also supported by a novel user-friendly design and evaluation tool that has been developed in MATLAB/Simulink that can speed-up the design, evaluation and comparison of analog and digital single-stage and time-interleaved variable bandpass sigma-delta modulators. This tool enables the user to specify the conversion type, topology, loop-filter type, path number and oversampling ratio.

Wireless Networks with Energy Harvesting and Power Transfer: Joint Power and Time Allocation

In this letter, we consider wireless powered communication networks which could operate perpetually, as the base station (BS) broadcasts energy to the multiple energy harvesting (EH) information transmitters. These employ “harvest then transmit” mechanism, as they spend all of their energy harvested during the previous BS energy broadcast to transmit the information towards the BS. Assuming time division multiple access (TDMA), we propose a novel transmission scheme for jointly optimal allocation of the BS broadcasting power and time sharing among the wireless nodes, which maximizes the overall network throughput, under the constraint of average transmit power and maximum transmit power at the BS. The proposed scheme significantly outperforms “state of the art” schemes that employ only the optimal time allocation. If a single EH transmitter is considered, we generalize the optimal solutions for the case of fixed circuit power consumption, which refers to a much more practical scenario.

Time-resolved dosimetric verification of respiratory-gated radiotherapy exposures using a high-resolution 2D ionisation chamber array

The aim of this work was to track and verify the delivery of respiratory-gated irradiations, performed with three versions of TrueBeam linac, using a novel phantom arrangement that combined the OCTAVIUS® SRS 1000 array with a moving platform. The platform was programmed to generate sinusoidal motion of the array. This motion was tracked using the real-time position management (RPM) system and four amplitude gating options were employed to interrupt MV beam delivery when the platform was not located within set limits. Time-resolved spatial information extracted from analysis of x-ray fluences measured by the array was compared to the programmed motion of the platform and to the trace recorded by the RPM system during the delivery of the x-ray field. Temporal data recorded by the phantom and the RPM system were validated against trajectory log files, recorded by the linac during the irradiation, as well as oscilloscope waveforms recorded from the linac target signal. Gamma analysis was employed to compare time-integrated 2D x-ray dose fluences with theoretical fluences derived from the probability density function for each of the gating settings applied, where gamma criteria of 2%/2 mm, 1%/1 mm and 0.5%/0.5 mm were used to evaluate the limitations of the RPM system. Excellent agreement was observed in the analysis of spatial information extracted from the SRS 1000 array measurements. Comparisons of the average platform position with the expected position indicated absolute deviations of  <0.5 mm for all four gating settings. Differences were observed when comparing time-resolved beam-on data stored in the RPM files and trajectory logs to the true target signal waveforms. Trajectory log files underestimated the cycle time between consecutive beam-on windows by 10.0  ±  0.8 ms. All measured fluences achieved 100% pass-rates using gamma criteria of 2%/2 mm and 50% of the fluences achieved pass-rates  >90% when criteria of 0.5%/0.5 mm were used. Results using this novel phantom arrangement indicate that the RPM system is capable of accurately gating x-ray exposure during the delivery of a fixed-field treatment beam.

Deep Corals, Deep Learning: Moving the Deep Net Towards Real-Time Image Annotation

The mismatch between human capacity and the acquisition of Big Data such as Earth imagery undermines commitments to Convention on Biological Diversity (CBD) and Aichi targets. Artificial intelligence (AI) solutions to Big Data issues are urgently needed as these could prove to be faster, more accurate, and cheaper. Reducing costs of managing protected areas in remote deep waters and in the High Seas is of great importance, and this is a realm where autonomous technology will be transformative.

Fixed-boundary constituencies and the principle of equal representation in Ireland

The process of constituency boundary revision in Ireland, designed to satisfy what is perceived as a rigid requirement that a uniform deputy-population ratio be maintained across constituencies, has traditionally consumed a great deal of the time of politicians and officials. For almost two decades after a High Court ruling in 1961, the process was a political one, was highly contentious, and was marked by serious allegations of ministerial gerrymandering. The introduction in 1979 of constituency commissions made up of officials neutralised, for the most part, charges that the system had become too politicised, but it continued the process of micro-management of constituency boundaries. This article suggests that the continuing problems caused by this system – notably, the permanently changing nature of constituency boundaries and resulting difficulties of geographical identification – could be resolved by reversion to the procedure that is normal in proportional representation systems: periodic post-census allocation of seats to constituencies whose boundaries are based on those of recognised local government units and which are stable over time. This reform, replacing the principle of redistricting by the principle of reapportionment, would result in more recognisable constituencies, more predictable boundary trajectories over time, and a more efficient, fairer, and speedier process of revision.

Applicazione ai gruppi di Lie della prolungabilità per Equazioni Differenziali Ordinarie

Lo scopo di questa tesi è studiare in dettaglio l'articolo "A Completeness Result for Time-Dependent Vector Fields and Applications" di Stefano Biagi e Andrea Bonfiglioli, dove si ottiene una condizione sufficiente per la completezza di un campo vettoriale (dipendente dal tempo) in RN, che generalizza la ben nota condizione di invarianza a sinistra per i gruppi di Lie.

Survivorship and Clinical Outcome of the Minimally Invasive Uniglide Medial Fixed Bearing, All-polyethylene Tibia, Unicompartmental Knee Arthroplasty at a Mean Follow-up of 7.3 Years

Background: Medial UKA performed in England and Wales represents 7 to 11% of all knee arthroplasty procedures, and is most commonly performed using mobile-bearing designs. Fixed bearing eliminates the risk of bearing dislocation, however some studies have shown higher revision rates for all-polyethylene tibial components compared to those that utilize metal-backed implants. The aim of the study is to analyse survivorship and maximum 8-year clinical outcome of medial fixed bearing, Uniglide unicompartmental knee arthroplasty performed using an all-polyethylene tibial component with a minimal invasive approach. Methods: Between 2002 and 2009, 270 medial fixed UKAs were performed in our unit. Patients were reviewed pre-operatively, 5 and 8 years post-operatively. Clinical and radiographic reviews were carried out. Patients’ outcome scores (Oxford, WOMAC and American Knee Score) were documented in our database and analysed. Results: Survival and clinical outcome data of 236 knees with a mean 7.3 years follow-up are reported. Every patient with less than 4.93 years follow-up underwent a revision. The patients’ average age at the time of surgery was 69.5 years. The American Knee Society Pain and Function scores, the Oxford Knee Score and the WOMAC score all improved significantly. The 5 years survival rate was 94.1% with implant revision surgery as an end point. The estimated 10 years survival rate is 91.3%. 14 patients were revised before the 5 year follow-up. Conclusion: Fixed bearing Uniglide UKA with an all-polyethylene tibial component is a valuable tool in the management of a medial compartment osteoarthritis, affording good short term survivorship.

Asymptotic Change-Point Analysis of the Dependencies in Time Series

In recent papers, Wied and his coauthors have introduced change-point procedures to detect and estimate structural breaks in the correlation between time series. To prove the asymptotic distribution of the test statistic and stopping time as well as the change-point estimation rate, they use an extended functional Delta method and assume nearly constant expectations and variances of the time series. In this thesis, we allow asymptotically infinitely many structural breaks in the means and variances of the time series. For this setting, we present test statistics and stopping times which are used to determine whether or not the correlation between two time series is and stays constant, respectively. Additionally, we consider estimates for change-points in the correlations. The employed nonparametric statistics depend on the means and variances. These (nuisance) parameters are replaced by estimates in the course of this thesis. We avoid assuming a fixed form of these estimates but rather we use "blackbox" estimates, i.e. we derive results under assumptions that these estimates fulfill. These results are supplement with examples. This thesis is organized in seven sections. In Section 1, we motivate the issue and present the mathematical model. In Section 2, we consider a posteriori and sequential testing procedures, and investigate convergence rates for change-point estimation, always assuming that the means and the variances of the time series are known. In the following sections, the assumptions of known means and variances are relaxed. In Section 3, we present the assumptions for the mean and variance estimates that we will use for the mean in Section 4, for the variance in Section 5, and for both parameters in Section 6. Finally, in Section 7, a simulation study illustrates the finite sample behaviors of some testing procedures and estimates.

Factors affecting fertility in frozen-thawed boar sperm

Frozen-thawed boar sperm holds the potential to have an impact on the future of the swine industry. Utilization of this technology could improve a swine producer’s ability to access top-tier genetics from around the world, to improve efficiency, profitability, and the quality of product to meet consumer demands. Effective application of frozen-thawed sperm can help reduce the potential risk associated with devastating economic loss due to the spread of disease. Frozen storage of boar sperm also provides a safeguard in the event of disease outbreaks, as genetic material from paternal lines can be preserved and banked for repopulation purposes. Historically these benefits have been masked by reduction in fertility measures such as litter size. The reduced fertility results from the damage sustained by the sperm cell during cryopreservation. However, increased understanding of this damage has lead to improved cryopreservation methods, ultimately increasing post-thaw viability and fertility. Enhancements in breeding technology have also resulted in a better understanding of the AI methods required to achieve acceptable farrowing rates and litter size. Fertility following AI with frozen-thawed sperm is approaching that of liquid stored sperm, and producers may soon reap the benefits of this technology. This thesis will outline the current swine industry, opportunities for utilizing frozen-thawed sperm, the main components of sperm, why they are susceptible to damage, and current freezing and breeding practices. Objective 1 was to develop a cryopreservation protocol for our lab that resulted in consistent post-thaw motility ( ≥ 40%) that would eventually be used by Illinois boar studs for domestic and international sale of frozen sperm. Evaluation with both manual microscopy and CASA methods were conducted to verify quality. A preliminary breeding trial was then conducted to test the fertility of sperm frozen with this method. There were 41 ejaculates from 23 boars used for freezing. Sperm were frozen at 1.4x109 sperm/mL, averaging 55.61.1% (meanSE) motility, following thaw. The samples assessed were not different (P>0.05) in motility when compared with manual or CASA systems, and results were most reliable at a 1:40 sperm dilution. In the preliminary breeding trial, gilts (n=14) were inseminated with either a single (n=10) or double (n=4) AI using 1, 2, or 4x109 motile, frozen-thawed sperm. Overall, the resulting pregnancy rates averaged 71.4% and numbers of normal fetuses per litter averaged 15.51.3 per litter. A feasibility study for freezing cost per ejaculate was estimated at $275/ejaculate or $11/dose of frozen-thawed semen at standard doses of 5x109 total frozen-thawed sperm. This cost estimate did not include genetic value, fixed equipment costs, depreciation, or variable lab space fees. Objective 2 focused on the proper methods for breeding with frozen-thawed boar sperm to achieve fertility. Our hypothesis was that increased numbers of inseminations and increased numbers of motile frozen-thawed sperm would improve pregnancy rate and litter size. Results showed acceptable fertility at high sperm numbers, but also the optimal method for insemination with the lowest dose tested. Gilts (n=111) responded to synchronization methods and were bred with 1, 2, or 4x109 motile frozen-thawed sperm from six boars using a single AI at 32 h, or a double AI, with the first AI at 24 and 32 h following estrus. Ultrasound was conducted at 12 h intervals to estimate the time of ovulation. On day 32 of gestation, overall pregnancy rate (73%) and number of normal fetuses per litter (10.80.5) across all treatments did not differ, and were not affected by number of motile sperm, or the interaction of number of motile sperm and number of inseminations. However, the number of inseminations tended to affect (P=0.14) the number of normal fetuses. Litter size increased with a double AI compared to single AI. Multiple inseminations helped to allow insemination to occur close to ovulation in response to variation in the time of ovulation. Both pregnancy rate and number of normal fetuses were greater when the time of the AI at 32 h occurred closer to the estimated time of ovulation (P<0.05). In addition, other factors such as presence of an abnormal ovary at day 30 decreased (P<0.001) pregnancy rate, while boar affected number of normal fetuses (P<0.01). Analysis of our data using a fertility index revealed doses of 2x109 motile sperm with multiple AI can achieve acceptable fertility with use of less sperm, when compared to AI using 4x109 motile sperm. The methods described here will investigate the potential for improved fertility when using frozen-thawed sperm, while accounting for variation in time of ovulation.

Reator de leito estruturado com recirculação submetido à aeração intermitente no tratamento de esgoto sanitário

The release of nitrogen compounds in water bodies can result in many environmental problems, so treat wastewater, such as sewage in order to remove not only organic matter but also nitrogen has been studied a few decades. From the above, the objective of this study was to evaluate the performance of a structured bed reactor, continuous flow, with recirculation, in removing organic matter and nitrogen present in wastewater under different cycles of intermittent aeration (AI) and to evaluate the influence of these cycles in the development of nitrifying bacteria (Oxidizing Bacteria Ammonia - BOA and Bacteria Oxidizing Nitrite - BON) and denitrifying (DESN) adhered (Support Material - MS) and suspension (Effluent - EF and sludge - LD). The reactor used has usable volume of 9.4 L. As support materials (MS) polyurethane foam was used, cut and fixed in PVC rods. 3 were worked aeration phases (AE) and non-aeration (AN) at different stage: Stage 1 (4 h EA / AN 2H); Stage 2 (2H EA / AN 1 h) and Phase 3 (2H EA / AN 2 h). During all hydraulic detention time phases was kept at 16 h and the effluent recirculated at a rate of 3 times the inflow. Were analyzed: pH, total alkalinity, temperature, chemical oxygen demand (COD), Biochemical Oxygen Demand (BOD), nitrogen Kjeldhl Total (NKT), ammonia-N-N-NH4+, nitrito-N-NO2+andnitrato-NO3-. The concentration of BOA, BON and DESN was determined using the number More Provável.gSSV-1 (NMP.gSSV-1). In phase 1 the percentage removal NTK N-NH4+ and NT was 76±10%, 70±21% and 67±10% respectively. In Phase 2 80±15% of removel NKT, 86±15% of N-NH4+ e 68±9% of removel NT e na Fase 3 de 58±20%, 72±28% and 41±6% of NKT, N-NH4+ of NT, respectively. The denitrification efficiency in stage 3 was over 70%, indicating that occurred in the reactor the process of simultaneous nitrification and denitrification (NDS). DQOT the removal percentages were 88 ± 4% in Phase 1, 94 ± 7 in Phase 2 and 90± 11% in Phase 3. The multivariate ANOVA applied to NMP.gSSV-1, it indicated that there was significant (F: 20,2, p <0,01) between the analyzed concentration of organisms AI in different cycles, but the differences between NMP.gSSV-1 depends not only isolated factors but of which means, and phase groups being analysis. From the results it is concluded that the working system is efficient in terms of nitrogen removal and organic matter, and that the stage with the highest availability of Dissolved Oxygen (DO) and C/N ratio (Step 2), was the one obtained the lower concentrations of organic matter effluents and N-NH4+. Hinted that there was a significant difference between the concentration (NMP.100mL-1) of the analyzed organizations (BOA, BON and DESN), but this difference does not depend on factors alone but of which means (MS, EF or LD), stages (1, 2 or 3) and groups (BOA, BON and DESN) is being considered.

Comparing fixed and flexible stocking as adaptations to inter-annual rainfall variability in the extensive beef industry of northern Australia

Many beef producers within the extensive cattle industry of northern Australia attempt to maintain a constant herd size from year-to-year (fixed stocking), whereas others adjust stock numbers to varying degrees annually in response to changes in forage supply. The effects of these strategies on pasture condition and cattle productivity cannot easily be assessed by grazing trials. Simulation studies, which include feedbacks of changes to pasture condition on cattle liveweight gain, can extend the results of grazing trials both spatially and temporally. They can compare a large number of strategies, over long periods of time, for a range of climate periods, at locations which differ markedly in climate. This simulation study compared the pasture condition and cattle productivity achieved by fixed stocking at the long-term carrying capacity with that of 55 flexible stocking strategies at 28 locations across Queensland and the Northern Territory. Flexible stocking strategies differed markedly in the degree they increased or decreased cattle stocking rates after good and poor pasture growing seasons, respectively. The 28 locations covered the full range in average annual rainfall and inter-annual rainfall variability experienced across northern Australia. Constrained flexibility, which limited increases in stocking rates after good growing seasons to 10% but decreased them by up to 20% after poor growing seasons, provides sustainable productivity gains for cattle producers in northern Australia. This strategy can improve pasture condition and increase cattle productivity relative to fixed stocking at the long-term carrying capacity, and its capacity to do this was greatest in the semiarid rangeland regions that contain the majority of beef cattle in northern Australia. More flexible stocking strategies, which also increased stocking rates after good growing seasons by only half as much as they decreased them after poor growing seasons, were equally sustainable and more productive than constrained flexibility, but are often impractical at property and industry scales. Strategies with the highest limits (e.g. 70%) for both annual increases and decreases in stocking rates could achieve higher cattle productivity, but this was at the expense of pasture condition and was not sustainable. Constrained flexible stocking, with a 10% limit for increases and a 20% limit for decreases in stocking rates annually, is a risk-averse adaptation to high and unpredictable rainfall variability for the extensive beef industry of northern Australia. © Australian Rangeland Society 2016.

JOINT ENERGY BEAMFORMING AND TIME ASSIGNMENT FOR COOPERATIVE WIRELESS POWERED NETWORKS

Wireless power transfer (WPT) and radio frequency (RF)-based energy har- vesting arouses a new wireless network paradigm termed as wireless powered com- munication network (WPCN), where some energy-constrained nodes are enabled to harvest energy from the RF signals transferred by other energy-sufficient nodes to support the communication operations in the network, which brings a promising approach for future energy-constrained wireless network design. In this paper, we focus on the optimal WPCN design. We consider a net- work composed of two communication groups, where the first group has sufficient power supply but no available bandwidth, and the second group has licensed band- width but very limited power to perform required information transmission. For such a system, we introduce the power and bandwidth cooperation between the two groups so that both group can accomplish their expected information delivering tasks. Multiple antennas are employed at the hybrid access point (H-AP) to en- hance both energy and information transfer efficiency and the cooperative relaying is employed to help the power-limited group to enhance its information transmission throughput. Compared with existing works, cooperative relaying, time assignment, power allocation, and energy beamforming are jointly designed in a single system. Firstly, we propose a cooperative transmission protocol for the considered system, where group 1 transmits some power to group 2 to help group 2 with information transmission and then group 2 gives some bandwidth to group 1 in return. Sec- ondly, to explore the information transmission performance limit of the system, we formulate two optimization problems to maximize the system weighted sum rate by jointly optimizing the time assignment, power allocation, and energy beamforming under two different power constraints, i.e., the fixed power constraint and the aver- age power constraint, respectively. In order to make the cooperation between the two groups meaningful and guarantee the quality of service (QoS) requirements of both groups, the minimal required data rates of the two groups are considered as constraints for the optimal system design. As both problems are non-convex and have no known solutions, we solve it by using proper variable substitutions and the semi-definite relaxation (SDR). We theoretically prove that our proposed solution method can guarantee to find the global optimal solution. Thirdly, consider that the WPCN has promising application potentials in future energy-constrained net- works, e.g., wireless sensor network (WSN), wireless body area network (WBAN) and Internet of Things (IoT), where the power consumption is very critical. We investigate the minimal power consumption optimal design for the considered co- operation WPCN. For this, we formulate an optimization problem to minimize the total consumed power by jointly optimizing the time assignment, power allocation, and energy beamforming under required data rate constraints. As the problem is also non-convex and has no known solutions, we solve it by using some variable substitutions and the SDR method. We also theoretically prove that our proposed solution method for the minimal power consumption design guarantees the global optimal solution. Extensive experimental results are provided to discuss the system performance behaviors, which provide some useful insights for future WPCN design. It shows that the average power constrained system achieves higher weighted sum rate than the fixed power constrained system. Besides, it also shows that in such a WPCN, relay should be placed closer to the multi-antenna H-AP to achieve higher weighted sum rate and consume lower total power.