A 100MHz to 1GHz, 0.35V to 1.5V supply 256 x 64 SRAM mock using symmetrized 9T SRAM cell with controlled read

In this paper, we present Dynamic Voltage and Frequency Managed 256 x 64 SRAM block in 65nm technology, for frequency ranging from 100MHz to 1GHz. The total energy is minimized for any operating frequency in the above range and leakage energy is minimized during standby mode. Since noise margin of SRAM cell deteriorates at low voltages, we propose Static Noise Margin improvement circuitry, which symmetrizes the SRAM cell by controlling the body bias of pull down NMOS transistor. We used a 9T SRAM cell that isolates Read and Hold Noise Margin and has less leakage. We have implemented an efficient technique of pushing address decoder into zigzag-super-cut-off in stand-by mode without affecting its performance in active mode of operation. The Read Bit Line (RBL) voltage drop is controlled and pre-charge of bit lines is done only when needed for reducing power wastage.

Atrial Electric Signal During Sinus Rhythm in Lone Paroxysmal Atrial Fibrillation

Atrial fibrillation (AF) is the most common tachyarrhythmia and is associated with substantial morbidity, increased mortality and cost. The treatment modalities of AF have increased, but results are still far from optimal. More individualized therapy may be beneficial. Aiming for this calls improved diagnostics. Aim of this study was to find non-invasive parameters obtained during sinus rhythm reflecting electrophysiological patterns related to propensity to AF and particularly to AF occurring without any associated heart disease, lone AF. Overall 240 subjects were enrolled, 136 patients with paroxysmal lone AF and 104 controls (mean age 45 years, 75% males). Signal measurements were performed by non-invasive magnetocardiography (MCG) and by invasive electroanatomic mapping (EAM). High-pass filtering techniques and a new method based on a surface gradient technique were adapted to analyze atrial MCG signal. The EAM was used to elucidate atrial activation in patients and as a reference for MCG. The results showed that MCG mapping is an accurate method to detect atrial electrophysiologic properties. In lone paroxysmal AF, duration of the atrial depolarization complex was marginally prolonged. The difference was more obvious in women and was also related to interatrial conduction patterns. In the focal type of AF (75%), the root mean square (RMS) amplitudes of the atrial signal were normal, but in AF without demonstrable triggers the late atrial RMS amplitudes were reduced. In addition, the atrial characteristics tended to remain similar even when examined several years after the first AF episodes. The intra-atrial recordings confirmed the occurrence of three distinct sites of electrical connection from right to left atrium (LA): the Bachmann bundle (BB), the margin of the fossa ovalis (FO), and the coronary sinus ostial area (CS). The propagation of atrial signal could also be evaluated non-invasively. Three MCG atrial wave types were identified, each of which represented a distinct interatrial activation pattern. In conclusion, in paroxysmal lone AF, active focal triggers are common, atrial depolarization is slightly prolonged, but with a normal amplitude, and the arrhythmia does not necessarily lead to electrical or mechanical dysfunction of the atria. In women the prolongation of atrial depolarization is more obvious. This may be related to gender differences in presentation of AF. A significant minority of patients with lone AF lack frequent focal triggers, and in them, the late atrial signal amplitude is reduced, possibly signifying a wider degenerative process in the LA. In lone AF, natural impulse propagation to LA during sinus rhythm goes through one or more of the principal pathways described. The BB is the most common route, but in one-third, the earliest LA activation occurs outside the BB. Susceptibility to paroxysmal lone AF is associated with propagation of the atrial signal via the margin of the FO or via multiple pathways. When conduction occurs via the BB, it is related with prolonged atrial activation. Thus, altered and alternative conduction pathways may contribute to pathogenesis of lone AF. There is growing evidence of variability in genesis of AF also within lone paroxysmal AF. Present study suggests that this variation may be reflected in cardiac signal pattern. Recognizing the distinct signal profiles may assist in understanding the pathogenesis of AF and identifying subgroups for patient-tailored therapy.

Microvascular reconstruction in extremity soft tissue sarcoma surgery

Soft tissue sarcomas (STS) are rare tumors of soft tissue occurring most frequently in the extremities. Modern treatment of extremity STS is based on limb-sparing surgery combined with radiotherapy. To prevent local recurrence, a healthy tissue margin of 2.5 cm around the resected tumor is required. This results in large defects of soft tissue and bone, necessitating the use of reconstructive surgery to achieve wound closure. When local or pedicled soft tissue flaps are unavailable, reconstruction with free flaps is used. Free flaps are elevated at a distant site, and have their blood flow restored at the recipient site through microvascular anastomosis. When limb-sparing surgery is made impossible, amputation is the only option. Proximal amputation such as forequarter amputation (FQA) causes considerable morbidity, but is nevertheless warranted for carefully selected patients for cure or palliation. 116 patients treated in 1985 - 2006 were included in the study. Of these, 93 patients treated with limb-sparing surgery and microvascular reconstructive surgery after resection of extremity STS. 25 patients who underwent FQA were also included. Patients were identified and their medical records retrospectively reviewed. In all, 105 free flap procedures were performed for 103 patients. A total of 95 curatively treated STS patients were included in survival analysis. The latissimus dorsi, used in 56% of cases, was the most frequently used free flap. Free flap success rate was 96%. There were 9% microvascular anastomosis complications and 15% wound complications. For curatively treated STS patients, local recurrence-free survival at 5 years was 73.1%, metastasis-free survival 58.3%, and overall disease-specific survival 68.9%. Functional results were good, with 75% of patients regaining normal or near-normal function after lower extremity, and 55% after upper extremity STS resection. Among curatively treated forequarter amputees, 5-year disease-free survival was 44%. In the palliatively treated group median time until disease death was 14 months. Microvascular reconstruction after extremity soft tissue sarcoma resection is safe and reliable, and produces well-healing wounds allowing early oncological treatment. Oncological outcome after these procedures is comparable to that of other extremity sarcoma patients. Functional results are generally good. Forequarter amputation is a useful treatment option for soft tissue tumors of the shoulder girdle and proximal upper extremity. When free flap coverage of extended forequarter amputation is required, the preferable flap is a fillet flap from the amputated extremity. Acceptable oncological outcome is achieved for curatively treated FQA patients. In the palliatively treated patient considerable periods of increased quality of life can be achieved.

Analysis of Energy Quantization Effects on Single-Electron Transistor Circuits

In this paper, the effects of energy quantization on different single-electron transistor (SET) circuits (logic inverter, current-biased circuits, and hybrid MOS-SET circuits) are analyzed through analytical modeling and Monte Carlo simulations. It is shown that energy quantizationmainly increases the Coulomb blockade area and Coulomb blockade oscillation periodicity, and thus, affects the SET circuit performance. A new model for the noise margin of the SET inverter is proposed, which includes the energy quantization effects. Using the noise margin as a metric, the robustness of the SET inverter is studied against the effects of energy quantization. An analytical expression is developed, which explicitly defines the maximum energy quantization (termed as ``quantization threshold'') that an SET inverter can withstand before its noise margin falls below a specified tolerance level. The effects of energy quantization are further studiedfor the current-biased negative differential resistance (NDR) circuitand hybrid SETMOS circuit. A new model for the conductance of NDR characteristics is also formulated that explains the energy quantization effects.

Merkel cell carcinoma : Epidemiological study with special reference to polyomavirus and vascular factors in pathogenesis

Merkel cell carcinoma (MCC) is a rare cutaneous malignancy that occurs predominantly on sun exposed skin areas. A new polyomavirus (MCPyV) was identified in MCC tumor tissues in 2008 suggesting that a viral infection might be an etiological factor. A typical MCC is a rapidly growing painless purple nodule. In its early stage it can be misjudged by its appearance as a cyst or abscess. Recurrences are common and approximately half of the patients will develop lymph node metastases and third of the patents will have distant metastases. It affects mostly elderly persons at an average age of 70 at the time of diagnosis. MCC was first described in 1972 and the first MCC patient in Finland was identified in 1983. MCC has been poorly recognized, but increased awareness and better diagnostic accuracy has increased the incidence since the early years. In this study, all cases with a notation of MCC during 1979 2008 were obtained from the Finnish Cancer Registry. Based on this data, the incidence is 0.11 for men and 0.12 for women. It is similar than that of other Nordic countries, but lower than in the USA. For clinical series, the files of patients diagnosed with MCC during 1983 2004 were reviewed, and the tissue samples were re-evaluated, if available (n=181). Third of the patients were men, and the most common site of the primary tumor was the head and neck (53%). The majority of the patients (86%) presented with a clinically node-negative (Stage I or II) disease, but the disease recurred in 38% of them. The treatment schemes were heterogeneous. No additional benefit from a wide margin (≥2 cm) was found compared to a margin of 0.1-1.9 cm, but intralesional excision was more often associated with local recurrence. None of the patients with Stage I-II disease who had received postoperative radiotherapy had local recurrence during the follow-up period. The 5-year relative survival ratio for Stage I disease was 68%, for Stage II 67%, for Stage III 16%, and for Stage IV 0%. The relative excess risk of death was significantly lower among women than among men. Some of these tissue samples were further analyzed for vascular invasion (n=126) by immunohistochemistry using vascular endothelial markers CD-31 and D2-40. Vascular invasion was seen in 93% of the samples and it was observed already in very small, <5mm tumors. The tissue samples were also analyzed for the presence of MCPyV by using a polymerase chain reaction (PCR) and quantitative PCR. MCPyV DNA was present in 80% of 114 samples studied. The patients with virus-positive tumors had better overall survival than patients with virus-negative tumors. Immunohistochemical analyses were performed for the expression of VEGFR-2 (n=21) and endostatin (n=19), but they had no prognostic value. Our results support the concept of treating MCC with margin-negative excision and radiotherapy to the tumor bed to reduce local recurrence. The finding of a high frequency of lymphovascular invasion reduces its value as a prognostic factor, but emphasizes the role of sentinel node biopsy even in very small primary MCC.

Geochemistry and petrology of the ferropicrite dikes and associated rocks of Vestfjella, western Dronning Maud Land, Antarctica

This study provides insights into the composition and origin of ferropicrite dikes (FeOtot = 13 17 wt. %; MgO = 13 19 wt. %) and associated meimechite, picrite, picrobasalt, and basalt dikes found at Vestfjella, western Dronning Maud Land, Antarctica. The dikes crosscut Jurassic Karoo continental flood basalts (CFB) that were emplaced during the early stages of the breakup of the Gondwana supercontinent ~180 Ma ago. Selected samples (31 overall from at least eleven dikes) were analyzed for their mineral chemical, major element, trace element, and Sr, Nd, Pb, and Os isotopic compositions. The studied samples can be divided into two geochemically distinct types: (1) The depleted type (24 samples from at least nine dikes) is relatively depleted in the most incompatible elements and exhibits isotopic characteristics (e.g., initial εNd of +4.8 to +8.3 and initial 187Os/188Os of 0.1256 0.1277 at 180 Ma) similar to those of mid-ocean ridge basalts (MORB); (2) The enriched type (7 samples from at least two dikes) exhibits relatively enriched incompatible element and isotopic characteristics (e.g., initial εNd of +1.8 to +3.6 and initial 187Os/188Os of 0.1401 0.1425 at 180 Ma) similar to those of oceanic island basalts. Both magma types have escaped significant contamination by the continental crust. The depleted type is related to the main phase of Karoo magmatism and originated as highly magnesian (MgO up to 25 wt. %) partial melts at high temperatures (mantle potential temperature >1600 °C) and pressures (~5 6 GPa) from a sublithospheric, water-bearing, depleted peridotite mantle source. The enriched type sampled pyroxene-bearing heterogeneities that can be traced down to either recycled oceanic crust or melt-metasomatized portions of the sublithospheric or lithospheric mantle. The source of the depleted type represents a sublithospheric end-member source for many Karoo lavas and has subsequently been sampled by the MORBs of the Indian Ocean. These observations, together with the purported high temperatures, indicate that the Karoo CFBs were formed in an extensive melting episode caused mainly by internal heating of the upper mantle beneath the Gondwana supercontinent. My research supports the view that ferropicritic melts can be generated in several ways: the relative Fe-enrichment of mantle partial melts is most readily achieved by (1) relatively low degree of partial melting, (2) high pressure of partial melting, and (3) melting of enriched source components (e.g., pyroxenite and metasomatized peridotite). Ferropicritic whole-rock compositions could also result from accumulation, secondary alteration, and fractional crystallization, however, and caution is required when addressing the parental magma composition.

Plant communities of field margins : the effects of management and environmental factors on species composition and diversity

Agri-environmental schemes have so far resulted in only minor positive implications for the biodiversity of agricultural environments, in contrast to what has been expected. Land-use intensification has decreased landscape heterogeneity and the amount of semi-natural habitats. Field margins are uncultivated areas of permanent vegetation located adjacent to fields. Since the number of these habitats is high, investing in their quality may result in more diverse agricultural landscapes. Field margins can be considered as multifunctional habitats providing agronomic, environmental and wildlife services. This thesis aimed at examining the plant communities of different types of field margin habitats and the factors affecting their species diversity and composition. The importance of edaphic, spatial and management factors was studied on regional, landscape and habitat scales. Vegetation surveys were conducted on regional and landscape scales and a field experiment on cutting management was conducted on a habitat scale. In field margin plant communities, species appeared to be indicators of high or intermediate soil fertility and moist soil conditions. The plant species diversity found was rather low, compared with most species-rich agricultural habitats in Finland, such as dry meadows. Among regions, land-use history, main production line, natural species and human induced distribution, climate and edaphic factors were elements inducing differences in species composition. The lowest regional species diversity of field margins was related to intensive and long-term cereal production. Management by cutting and removal or grazing had a positive effect on plant species diversity. The positive effect of cutting and removal on species richness was also dependent on the adjacent source of colonizing species. Therefore, in species-poor habitats and landscapes, establishment of margins with diverse seed mixtures can be recommended for enhancing the development of species richness. However, seed mixtures should include only native species preferably local origin. Management by cutting once a year for 5 years did not result in a decline in dominance of a harmful weed species, Elymus repens, showing that E. repens probably needs cutting more frequently than once per year. Agri-environmental schemes should include long-term contracts with farmers for the establishment, and management by cutting and removal or grazing, of field margins that are several metres wide. In such schemes, the timing and frequency of management should be planned so as not to harm other taxa, such as the insects and birds that are dependent on these habitats. All accidental herbicide drifts to field margins should be avoided when spraying the cultivated area to minimize the negative effects of sprayings on vegetation. The harmful effects of herbicides can be avoided by organic farming methods.

Dynamic security assessment of power systems using structure-preserving energy functions

An application of direct methods to dynamic security assessment of power systems using structure-preserving energy functions (SPEF) is presented. The transient energy margin (TEM) is used as an index for checking the stability of the system as well as ranking the contigencies based on their severity. The computation of the TEM requires the evaluation of the critical energy and the energy at fault clearing. Usually this is done by simulating the faulted trajectory, which is time-consuming. In this paper, a new algorithm which eliminates the faulted trajectory estimation is presented to calculate the TEM. The system equations and the SPEF are developed using the centre-of-inertia (COI) formulation and the loads are modelled as arbitrary functions of the respective bus voltages. The critical energy is evaluated using the potential energy boundary surface (PEBS) method. The method is illustrated by considering two realistic power system examples.

Semi-Supervised Classification Using Sparse Gaussian Process Regression

Gaussian Processes (GPs) are promising Bayesian methods for classification and regression problems. They have also been used for semi-supervised learning tasks. In this paper, we propose a new algorithm for solving semi-supervised binary classification problem using sparse GP regression (GPR) models. It is closely related to semi-supervised learning based on support vector regression (SVR) and maximum margin clustering. The proposed algorithm is simple and easy to implement. It gives a sparse solution directly unlike the SVR based algorithm. Also, the hyperparameters are estimated easily without resorting to expensive cross-validation technique. Use of sparse GPR model helps in making the proposed algorithm scalable. Preliminary results on synthetic and real-world data sets demonstrate the efficacy of the new algorithm.

Sensitive high-resolution ion microprobe U-Pb dating of prograde and retrograde ultrahigh-temperature metamorphism as exemplified by Sri Lankan granulites

Ultrahigh-temperature (UHT) granulites of the central Highland Complex, Sri Lanka, underwent some of the highest known peak temperatures of crustal metamorphism. Zircon and monazite U-Pb systems in granulites near Kandy, the highest grade region (similar to 1050 degrees C; 0.9 GPa), preserve both a record of the timing of prograde and retrograde phases of UHT metamorphism and evidence for the ages of older protolith components. Zircon grains from a quartz-saturated granulite containing relics of the peak UHT assemblage have remnant detrital cores with dates of ca. 2.5-0.83 Ga. Date clusters of ca. 1.7 and 1.04-0.83 Ga record episodes of zircon growth in the source region of the protolith sediment. Two generations of overgrowths with contrasting Th/U record metamorphic zircon growth at 569 +/- 5 and 551 +/- 7 Ma, probably in the absence and presence of monazite, respectively. The age of coexisting metamorphic monazite (547 +/- 7 Ma) is indistinguishable from that of the younger, low-Th/U zircon overgrowths. Zircon from a quartz-undersaturated monazite-absent UHT granulite with a mainly retrograde assemblage is mostly metamorphic (551 +/- 5 Ma). The ca. 570 Ma zircon overgrowths in the quartz-saturated granulite probably record partial melting just before or at the metamorphic peak. The ca. 550 Ma zircon in both rocks, and the ca. 550 Ma monazite in the quartz-saturated sample, record post-peak isothermal decompression. A possible model for this pressure-temperature-time evolution is ultrahot collisional orogeny during the assembly of Gondwana, locally superheated by basaltic underplating, followed by fast extensional exhumation.

Optimal Use of Treatment Modalities and Treatment Results of Osteosarcoma and Soft Tissue Sarcomas

Soft tissue sarcomas are malignant tumours of mesenchymal origin. Because of infiltrative growth pattern, simple enucleation of the tumour causes a high rate of local recurrence. Instead, these tumours should be resected with a rim of normal tissue around the tumour. Data on the adequate margin width are scarce. At Helsinki University Central Hospital (HUCH) a multidisciplinary treatment group started in 1987. Surgical resection with a wide margin (2.5 cm) is the primary aim. In case of narrower margin radiation therapy is necessary. The role of adjuvant chemotherapy remains unclear. Our aims were to study local control by the surgical margin and to develop a new prognostic tool to aid decision-making on which patients should receive adjuvant chemotherapy. Patients with soft tissue sarcoma of the extremity or the trunk wall referred to HUCH during 1987-2002 form material in Studies I and II. External validation material comes from the Lund university sarcoma registry. The smallest surgical margin of at least 2.5 centimetres yielded local control of 89 per cent at five years. Amputation rate was 9 per cent. The proposed prognostic model with necrosis, vascular invasion, size on a continuous scale, depth, location and grade worked well both in Helsinki material and in the validation material, and it also showed good calibration. Based on the present study, we recommend the smallest surgical margin of 2-3 centimetres in soft tissue sarcoma irrespective of grade. Improvement in local control was present but modest in margins wider than 1 centimetre. In cases where gaining a wider margin would lead to a considerable loss of function, smaller margin is to be considered combined to radiation therapy. Patients treated with inadequate margins should be offered radiation therapy irrespective of tumour grade. Our new prognostic model to estimate 10-year survival probability in patients with soft tissue sarcoma of the extremities or trunk wall showed good dicscrimination and calibration. For time being the prognostic model is available for scientific use and further validations. In the future, the model may aid in clinical decision-making. For operable osteosarcoma, neoadjuvant multidrug chemotherapy followed by delayed surgery and multidrug adjuvant chemotherapy is the treatment of choice. Overall survival rates at five years are approximately 75 per cent in modern trials with classical osteosarcoma. All patients diagnosed and reported to the Finnish Cancer Registry with osteosarcoma in Finland during 1971-2005 form the material in Studies III and IV. Limb-salvage rate increased from 23 per cent to 78 per cent during 1971-2005. The 10-year sarcoma-specific survival for the whole study population improved from 32 per cent to 62 per cent. It was 75 per cent for patients with a local high-grade osteosarcoma of the extremity diagnosed during 1991-2005. This study outlines the improved prognosis of osteosarcoma patients in Finland with modern chemotherapy. The 10-year survival rates are good also in an international scale. Nonetheless, their limb-salvage rate remains inferior to those seen for highly selected patient series. Overall, the centralisation of osteosarcoma treatment would most likely improve both survival and limb-salvage rates even further.

Meridional propagation of large-scale monsoon convective zones

Observational studies indicate that the convective activity of the monsoon systems undergo intraseasonal variations with multi-week time scales. The zone of maximum monsoon convection exhibits substantial transient behavior with successive propagating from the North Indian Ocean to the heated continent. Over South Asia the zone achieves its maximum intensity. These propagations may extend over 3000 km in latitude and perhaps twice the distance in longitude and remain as coherent entities for periods greater than 2-3 weeks. Attempts to explain this phenomena using simple ocean-atmosphere models of the monsoon system had concluded that the interactive ground hydrology so modifies the total heating of the atmosphere that a steady state solution is not possible, thus promoting lateral propagation. That is, the ground hydrology forces the total heating of the atmosphere and the vertical velocity to be slightly out of phase, causing a migration of the convection towards the region of maximum heating. Whereas the lateral scale of the variations produced by the Webster (1983) model were essentially correct, they occurred at twice the frequency of the observed events and were formed near the coastal margin, rather than over the ocean. Webster's (1983) model used to pose the theories was deficient in a number of aspects. Particularly, both the ground moisture content and the thermal inertia of the model were severely underestimated. At the same time, the sea surface temperatures produced by the model between the equator and the model's land-sea boundary were far too cool. Both the atmosphere and the ocean model were modified to include a better hydrological cycle and ocean structure. The convective events produced by the modified model possessed the observed frequency and were generated well south of the coastline. The improved simulation of monsoon variability allowed the hydrological cycle feedback to be generalized. It was found that monsoon variability was constrained to lie within the bounds of a positive gradient of a convective intensity potential (I). The function depends primarily on the surface temperature, the availability of moisture and the stability of the lower atmosphere which varies very slowly on the time scale of months. The oscillations of the monsoon perturb the mean convective intensity potential causing local enhancements of the gradient. These perturbations are caused by the hydrological feedbacks, discussed above, or by the modification of the air-sea fluxes caused by variations of the low level wind during convective events. The final result is the slow northward propagation of convection within an even slower convective regime. The ECMWF analyses show very similar behavior of the convective intensity potential. Although it is considered premature to use the model to conduct simulations of the African monsoon system, the ECMWF analysis indicates similar behavior in the convective intensity potential suggesting, at least, that the same processes control the low frequency structure of the African monsoon. The implications of the hypotheses on numerical weather prediction of monsoon phenomenon are discussed.

Evaluation and improvement of generators reactive power margins in interconnected power systems

The amount of reactive power margin available in a system determines its proximity to voltage instability under normal and emergency conditions. More the reactive power margin, better is the systems security and vice-versa. A hypothetical way of improving the reactive margin of a synchronous generator is to reduce the real power generation within its mega volt-ampere (MVA) ratings. This real power generation reduction will affect its power contract agreements entered in the electricity market. Owing to this, the benefit that the generator foregoes will have to be compensated by paying them some lost opportunity cost. The objective of this study is three fold. Firstly, the reactive power margins of the generators are evaluated. Secondly, they are improved using a reactive power optimization technique and optimally placed unified power flow controllers. Thirdly, the reactive power capacity exchanges along the tie-lines are evaluated under base case and improved conditions. A detailed analysis of all the reactive power sources and sinks scattered throughout the network is carried out in the study. Studies are carried out on a real life, three zone, 72-bus equivalent Indian southern grid considering normal and contingency conditions with base case operating point and optimised results presented.

Bounded Unpopularity Matchings

We investigate the following problem: given a set of jobs and a set of people with preferences over the jobs, what is the optimal way of matching people to jobs? Here we consider the notion of popularity. A matching M is popular if there is no matching M' such that more people prefer M' to M than the other way around. Determining whether a given instance admits a popular matching and, if so, finding one, was studied by Abraham et al. (SIAM J. Comput. 37(4):1030-1045, 2007). If there is no popular matching, a reasonable substitute is a matching whose unpopularity is bounded. We consider two measures of unpopularity-unpopularity factor denoted by u(M) and unpopularity margin denoted by g(M). McCutchen recently showed that computing a matching M with the minimum value of u(M) or g(M) is NP-hard, and that if G does not admit a popular matching, then we have u(M) >= 2 for all matchings M in G. Here we show that a matching M that achieves u(M) = 2 can be computed in O(m root n) time (where m is the number of edges in G and n is the number of nodes) provided a certain graph H admits a matching that matches all people. We also describe a sequence of graphs: H = H(2), H(3), ... , H(k) such that if H(k) admits a matching that matches all people, then we can compute in O(km root n) time a matching M such that u(M) <= k - 1 and g(M) <= n(1 - 2/k). Simulation results suggest that our algorithm finds a matching with low unpopularity in random instances.