Restricted Arc Research Articles

Comparison of photon energies and field techniques for ovarian dose reduction in volumetric modulated arc therapy

For fertility preservation in young female patients undergoing pelvic radiotherapy for cervical cancer, lateral ovarian transposition (LOT) is a procedure that moves the ovaries away from the radiation field. However, it is still challenging to fully protect the ovaries from radiation damage in volumetric modulated arc therapy (VMAT). In this study, we optimized VMAT techniques and simulated the effect of the LOT position on the ovarian dose. Ten cervical cancer patients who received pelvic radiotherapy after LOT were retrospectively analyzed. A restricted arc plus split field technique, which incorporated beam avoidance sectors, split field, fixed jaw, and orthogonal collimator orientation with 10 MV energy (rasf-10MV-VMAT), was designed to minimize the dose to the ovaries. This technique was compared with dual-arc conventional VMAT (dac-6MV-VMAT) and restricted arc and field VMAT (raf-6MV-VMAT) techniques with 6 MV energy. Ovarian dose, target coverage, and organs at risk (OAR) sparing were compared. The location of the ovaries in the anterior-posterior and superior-inferior directions was changed to simulate the effect of the LOT position on the ovarian dose. Compared to dac-6MV-VMAT and raf-6MV-VMAT, rasf-10MV-VMAT decreased the ovarian dose significantly more, especially for a low-dose volume. Both ovaries, received a 44.0–52.1 % lower volume of >3 Gy dose, and (0.5–1.9 Gy) lower maximum and mean doses with rasf-10MV-VMAT (p < 0.05). Rasf-10MV-VMAT also improved target conformity and coverage more than raf-6MV-VMAT (p < 0.05) and reduced the bladder mean dose more than dac-6MV-VMAT (p < 0.05). The ovarian dose decreased with the distance from the target contour, and placing the ovaries near the mid-frontal plane or as high as possible after the LOT lowered ovarian exposure. This technique, using 10 MV photon energy combined with field technique optimization, reduced the ovarian dose, particularly by decreasing the low-dose exposure of ovarian tissue and improving the target conformity simultaneously. The ovarian dose could be minimized by a proper LOT position. This optimized technique could enhance ovarian protection and fertility preservation for young female survivors of cervical cancer.

Restricted Arc Connectivity of Unidirectional Hypercubes and Unidirectional Folded Hypercubes

Unidirectional hypercubes and unidirectional folded hypercubes are generalizations of hypercubes and folded hypercubes to digraphs. The super-$\lambda$ property of a digraph is a index for network reliability, which can be measured by the restricted arc-connectivity quantitatively. In this paper, we first show that the restricted arc-connectivity of the $n$-dimensional unidirectional hypercube is $n-1$ when $n$ is even and is $n-2$ when $n$ is odd, and then we show that the restricted arc-connectivity of the $n$-dimensional unidirectional folded hypercube is $n-1$ when $n$ is even and is $n$ when $n$ is odd. As a consequence, we prove that both unidirectional hypercube and unidirectional folded hypercube are super-$\lambda$.

The plasma morphology of an asymmetric electrode ablative pulsed plasma thruster

The ablative pulsed plasma thruster (APPT) is a typical form of electric propulsion that is highly suitable for micro-satellites. However, its low performance has been a main drawback. Recently, an asymmetric segmented anode schematic was shown to enhance the performance of APPTs. The improved thrust performance obtained with the use of a segmented anode can potentially enable promising applications in future space tasks. To further understand the physical processes behind a segmented anode APPT, experiments using an ultra-high-speed camera, narrow bandpass filters, and a magnetic probe were conducted with both normal parallel-plate electrodes and a segmented anode on an experimental APPT. Successive images of light emission from C+, neutral C2, and broadband emission reveal the evolution of the plasma morphology on an APPT with a segmented anode. The magnetic field strength profiles show that the inter-electrode plasma propagation velocity of a segmented anode APPT is approximately 19 km s−1, which is slightly lower than that of a normal APPT at 23 km s−1. However, the similar order of magnitude suggests a similar downstream acceleration mechanism between the two. The arc morphology observed in the high-speed images shows that the segmented anode APPT with asymmetric electrodes has a restricted arc attachment point, possibly resulting in stronger arc current density at the anode corner. This should result in higher ionization and ablation when compared with a normal anode APPT. Based on the results here, we hypothesize that the segmented anode APPT may be able to better utilize the restrike energy in the propellant ionization process. This fundamentally changes the physical process behind APPT operation, meaning that the improvements should also be applicable to other APPT designs. It can also be adopted as an additional step in the overall optimization of an APPT design.

Cartesian product digraphs with optimal restricted arc connectivity

The restricted arc connectivity of digraphs is a generalization of arc connectivity. In 2009, Chen and Liu [2] showed an upper bound on the restricted arc connectivity for Cartesian product digraphs. In this paper, we present a sufficient condition for this upper bound to be attained. Furthermore, we give an example to show that our result is best possible.

A Comparative Study on the Long-Term Outcome of Total Knee Arthroplasty Performed for Knees Stiff in Extension and Those Stiff in Flexion

BackgroundPatients with chronic stiff knee with extremely restricted arc of motion (AOM ≤ 20°) may present with stiffness either in extension (stiff in extension [SE]) or in flexion (stiff in flexion [SF]). The difference in the functional outcome after total knee arthroplasty between these 2 groups has not been elaborated in literature. MethodsWe retrospectively analyzed 96 patients (115 knees), who had undergone total knee arthroplasty between January 1990 and December 2010 for stiff or spontaneously ankylosed knees (AOM ≤ 20°). This included 51 knees in SE group and 64 knees in SF group. ResultsThe average duration of follow-up was 9.7 years (2-17.5 years). The total AOM improved from an average of 10.9° ± 7.4° preoperatively to 86.5° ± 13.5° postoperatively in SE group and 8.7° ± 6.8° to 92.2° ± 16.8° in the SF group. The mean Knee Society Score in the SE group improved from 23.2 ± 5.7 preoperatively to 74.1 ± 8.9 postoperatively and that of SF group from 14 ± 5.2 to 71.2 ± 12.5. At 3 months follow-up, Knee Society Score for SE group were higher than that for SF group (P = .03). This difference was not noted beyond 1 year. Complications were noted in 24 (20.9%) knees—10 (23.5%) in SE group and 14 (21.9%) in SF group. ConclusionThe maximum mean AOM achieved was higher in SF group but the incidence of residual flexion contracture was also higher as compared to SE group. The long-term functional outcome scores in SE and SF groups are similar.

3-Restricted arc connectivity of digraphs

The k-restricted arc connectivity of digraphs is a common generalization of the arc connectivity and the restricted arc connectivity. An arc subset S of a strong digraph D is a k-restricted arc cut if D−S has a strong component D′ with order at least k such that D−V(D′) contains a connected subdigraph with order at least k. The k-restricted arc connectivity λk(D) of a digraph D is the minimum cardinality over all k-restricted arc cuts of D.Let D be a strong digraph with order n≥6 and minimum degree δ(D). In this paper, we first show that λ3(D) exists if δ(D)≥3 and, furthermore, λ3(D)≤ξ3(D) if δ(D)≥4, where ξ3(D) is the minimum 3-degree of D. Next, we prove that λ3(D)=ξ3(D) if δ(D)≥n+32. Finally, we give examples showing that these results are best possible in some sense.

Designing granular solution methods for routing problems with time windows

The use of granular neighborhoods is one way to improve the run-time of local-search-based metaheuristics for combinatorial optimization problems without compromising solution quality. So-called sparsification methods are applied to restrict the neighborhoods to include only elements which are likely to be part of high-quality solutions. The goal of this work is to provide insights about the design of effective and efficient granular solution methods for routing problems with time windows. In extensive numerical experiments with a granular tabu search (GTS) for the vehicle-routing problem with time windows (VRPTW), we find that sparsification methods using reduced-cost values based on the solution of a linear relaxation of the original problem outperform standard sparsification methods. Furthermore, including additional depot arcs into the restricted arc set (beyond those selected by the sparsification method) improves solution quality. The same is true for dynamically inserting into the restricted arc set (i) the arcs involved in the best move selected in each iteration, and (ii) the arcs of the current best-known solution. Moreover, for small restricted arc sets, guaranteeing a minimum number of incoming and outgoing arcs per vertex is beneficial. Finally, dynamically altering the size of the restricted arc set can be used to successfully diversify and intensify the search, which has a significant positive effect on solution quality. The usefulness of the gained insights about the design of granular solution methods is demonstrated by the performance of the final configuration of our GTS for VRPTW, which obtains state-of-the-art results and reaches an outstanding computational efficiency.

Are There Risk Factors for Complications of Perforator-based Propeller Flaps for Lower-extremity Reconstruction?

Conventional pedicled flaps for soft tissue reconstruction of lower extremities have shortcomings, including donor-site morbidity, restricted arc of rotation, and poor cosmetic results. Propeller flaps offer several potential advantages, including no need for microvascular anastomosis and low impact on donor sites, but their drawbacks have not been fully characterized. We assessed (1) frequency and types of complications after perforator-based propeller flap reconstruction in the lower extremity and (2) association of complications with arc of rotation, flap dimensions, and other potential risk factors. From 2007 to 2012, 74 patients (44 males, 30 females), 14 to 87years old, underwent soft tissue reconstruction of the lower extremities with propeller flaps. General indications for this flap were wounds and small- and medium-sized defects located in distal areas of the lower extremity, not suitable for coverage with myocutaneous or muscle pedicled flaps. This group represented 26% (74 of 283) of patients treated with vascularized coverage procedures for soft tissue defects in the lower limb during the study period. Minimum followup was 1year (mean, 3years; range, 1-7years); eight patients (11%) were lost to followup before 1year. Complications and potential risk factors, including arc of rotation, flap dimensions, age, sex, defect etiology, smoking, diabetes, and peripheral vascular disease, were recorded based on chart review. Twenty-eight of 66 flaps (42%) had complications. Venous congestion (11 of 66, 17%) and superficial necrosis (seven of 66, 11%) occurred most frequently. Eighteen of the 28 complications (64%) healed with no further treatment; eight patients (29%) underwent skin grafting, and one patient each experienced total flap failure (2%) and partial flap failure (2%). In those patients, a free anterolateral thigh flap was used as the salvage procedure. No correlations were found between complications and any potential risk factor. We were not able to identify any specific risk factors related to complications, and future multicenter studies will be necessary to determine which patients or wounds are at risk of complications. Propeller flaps had a low failure rate and risk of secondary surgery. These flaps are particularly useful for covering small- and medium-sized defects in the distal leg and Achilles tendon region and are a reliable and effective alternative to free flaps. Level IV, therapeutic study. See the Instructions for Authors for a complete description of levels of evidence.

Midcarpal Fusion Is Also Indicated in Patients With Advanced Carpal Collapse and Already Highly Restricted Range of Motion Preoperatively

Although midcarpal fusion is a well-accepted treatment of advanced carpal collapse, 1 question remains unanswered: is this technically demanding procedure worthwhile in wrists with an already highly restricted flexion-extension arc (FEA) of less than 60 degrees preoperatively? Therefore, a retrospective analysis of the records of 142 consecutive patients who had had a midcarpal fusion of the wrist was performed. There were 50 patients in group 1 (FEA < 60 degrees) and 92 patients in group 2 (FEA ≥ 60 degrees) with a mean follow-up of 23 months. Flexion-extension arc preoperatively and postoperatively, pain evaluated by a visual analog scale from 0 to 10 as well as the patients' upper extremity functioning captured with the Disabilities of the Arm, Shoulder and Hand questionnaire were statistically analyzed. Functional range of motion was defined as 5-degree wrist flexion and 30-degree wrist extension. Median wrist flexion before versus after midcarpal fusion was 18 versus 22 degrees and 23 versus 25 degrees for wrist extension in group 1. In group 2, the data were 42 versus 27 degrees and 43 versus 30 degrees, respectively. Midcarpal fusion led to an improvement of FEA in 52% of patients in group 1 but only in 5.4% of patients in group 2. In group 1, the median FEA improved by 122%, whereas the median FEA declined to 69% in group 2. Preoperatively 20% of patients in group 1 and 95% of patients in group 2 reached a functional range of motion for flexion/extension, which changed to 36% in group 1 versus 62% in group 2 postoperatively. The visual analog scale score improved for group 1 from 5.7 to 2.4 and for group 2 from 5.7 to 3.2, respectively. The postoperative DASH score was for both groups 33 points. Our data demonstrate that even in patients with a highly restricted range of motion in advanced carpal collapse, it is still reasonable to perform a midcarpal fusion instead of total wrist fusion.

Biphasic assembly of the contractile apparatus during the first two cell division cycles in zebrafish embryos

The large and optically clear embryos of the zebrafish provide an excellent model system in which to study the dynamic assembly of the essential contractile band components, actin and myosin, via double fluorescent labelling in combination with confocal microscopy. We report the rapid appearance (i.e. within <2 min) of a restricted arc of F-actin patches along the prospective furrow plane in a central, apical region of the blastodisc cortex. These patches then fused with each other end-to-end forming multiple actin cables, which were subsequently bundled together forming an F-actin band. During this initial assembly phase, the F-actin-based structure did not elongate laterally, but was still restricted to an arc extending ~15° either side of the blastodisc apex. This initial assembly phase was then followed by an extension phase, where additional F-actin patches were added to each end of the original arc, thus extending it out to the edges of the blastodisc. The dynamics of phosphorylated myosin light chain 2 (MLC2) recruitment to this F-actin scaffold also reflect the two-phase nature of the contractile apparatus assembly. MLC2 was not associated with the initial F-actin arc, but MLC2 clusters were recruited and assembled into the extending ends of the band. We propose that the MLC2-free central region of the contractile apparatus acts to position and then extend the cleavage furrow in the correct plane, while the actomyosin ends alone generate the force required for furrow ingression. This biphasic assembly strategy may be required to successfully divide the early cells of large embryos.

Slow motions in the hydrophobic core of chicken villin headpiece subdomain and their contributions to configurational entropy and heat capacity from solid-state deuteron NMR measurements.

We have investigated microsecond to millisecond time scale dynamics in several key hydrophobic core methyl groups of chicken villin headpiece subdomain protein (HP36) using a combination of single-site labeling, deuteron solid-state NMR line shape analysis, and computational modeling. Deuteron line shapes of hydrated powder samples are dominated by rotameric jumps and show a large variability of rate constants, activation energies, and rotameric populations. Site-specific activation energies vary from 6 to 38 kJ/mol. An additional mode of diffusion on a restricted arc is significant for some sites. In dry samples, the dynamics is quenched. Parameters of the motional models allow for calculations of configurational entropy and heat capacity, which, together with the rate constants, allow for observation of interplay between thermodynamic and kinetic picture of the landscape. Mutations at key phenylalanine residues at both distal (F47L&F51L) and proximal (F58L) locations to a relatively rigid side chain of L69 have a pronounced effect on alleviating the rigidity of this side chain at room temperature and demonstrate the sensitivity of the hydrophobic core environment to such perturbations.

Probing the Dynamics of a Protein Hydrophobic Core by Deuteron Solid-State Nuclear Magnetic Resonance Spectroscopy

With the goal of investigating dynamical features of hydrophobic cores of proteins over a wide range of temperatures, the chicken villin headpiece subdomain protein (HP36) was labeled at a "single" site corresponding to any one of the two C(delta)D(3) groups of leucine-69, which is located in a key position of the core. The main techniques employed are deuteron NMR quadrupolar echo line shape analysis, and T(1Z) (Zeeman) and T(1Q) (quadrupolar order) relaxation experiments performed at 11.7 and 17.6 T over the temperature range of 112 to 298 K. The experimental data are compared with computer simulations. The deuteron line shapes give an excellent fit to a three-mode motional model that consists of (a) fast three-site rotational jumps about the pseudo C(3) methyl spinning axis, (b) slower reorientation of the spinning axis, described by diffusion along a restricted arc, and (c) large angle jumps between traces of rotameric conformers. Relaxation behavior is described by a phenomenological distribution of activation energies for three-site hops at high temperatures that collapses to a single, distinctly smaller value for lower temperatures.

The restricted arc connectivity of Cartesian product digraphs

For a strongly connected digraph D = ( V ( D ) , A ( D ) ) , an arc set S ⊆ A ( D ) is a k-restricted arc cut if D − S has a non-trivial strongly connected component D 1 such that D − V ( D 1 ) contains an arc. The restricted arc connectivity λ ′ ( D ) is the minimum cardinality of all restricted arc-cuts. In this paper we prove that Cartesian product digraph D = D 1 × D 2 of two strongly connected digraphs D 1 and D 2 is λ ′ -connected. We also give an upper and lower bound for λ ′ ( D ) , respectively. Furthermore, we obtain that λ ′ ( C m → × C n → ) = min { m , n , 3 } and λ ′ ( C m → × K n → ) = n .

Reconstruction in the buttock region using the local fasciocutaneous infragluteal (FCI) flap

Defects in the buttock region are frequent indications for plastic surgery and are caused by various mechanisms. Therefore, different flaps were introduced and are well established. However, all of them have their limitations in reconstruction because of their restricted arc of rotation. Hence, we indicated the use of the local fasciocutaneous infragluteal (FCI) flap for reconstruction of such defects in the buttock region. In a series of 14 patients, three of them being paraplegics, the authors used 15 local FCI flaps to cover defects in the buttock region. The defects were caused by pressure sores, pilonidal sinus infection with recurrence, an adenocarcinoma of the gluteal region, a massive abscess after intramuscular gluteal injection, lipodystrophy of the lateral gluteal region and by multiple operations after an infection of implanted hip-joint prosthesis. The median dimension of the flaps was 177 cm(2). Fourteen of the 15 flaps healed uneventfully. In one patient, a re-mobilisation of the flap was necessary after a minor, distal-flap necrosis. Closure of the donor site was possible in all patients without further trouble. One patient needed a second local FCI flap because of a new pressure sore on the contralateral sacral region. The FCI flap is not only a versatile and reliable free flap with different indications, but is also a good alternative as a local flap for defect reconstruction in the whole buttock region, as demonstrated in this study for the first time. It can be raised as a sensate flap without restrictions of mobility in ambulatory patients. The donor-site morbidity is minimal, and options for future flaps of the gluteal region are preserved.

Special Paper: Major Gold Deposits and Belts of the North and South American Cordillera: Distribution, Tectonomagmatic Settings, and Metallogenic Considerations

A compilation of economically viable gold concentrations containing ≥10 Moz in the North and South American Cordillera reveals the existence of 22 discrete belts in addition to five major isolated deposits, most formed over the last 150 m.y. The gold concentrations are attributed to eight widely recognized deposit types, of which porphyry, sediment-hosted, and high-sulfidation epithermal are economically the most important. Individual gold belts are typically several tens to hundreds of kilometers long, dominated by single deposit types, and metallogenically active for relatively brief periods (<5–20 m.y.). Many of the gold belts and major isolated deposits were generated under extensional or transtensional tectonic conditions in either arc or back-arc settings. Nevertheless, the two main high-sulfidation epithermal gold belts were generated in thickening or already-thickened crust during low-angle subduction. Eight other gold belts or districts also accompanied compression or transpression, with two of them, the main orogenic gold belts, occupying fore-arc sites. There is a strong suggestion that the preeminent Cordilleran gold concentrations formed either during or immediately following prolonged contraction. The major gold deposits and belts occur along the craton edge as well as in adjoining accreted terranes, but almost all are of postaccretionary timing. Many of the gold belts and isolated deposits were localized by crustal-scale faults or lineaments, which may be either parallel or transverse to the Cordilleran margin. The gold concentrations accumulated during active subduction, commonly in close spatial and temporal association with intermediate to felsic, medium- to high-K calc-alkaline igneous rocks. By contrast, the low-sulfidation epithermal gold deposits accompany bimodal volcanic pulses of calc-alkaline, tholeiitic, or alkaline affinity. However, a gold-alkaline rock association is uncommon. A genetic link between gold mineralization and coeval magmatism is widely accepted for most of the deposit types, the exceptions being the sediment-hosted and orogenic gold deposits. Notwithstanding the small cumulative extent of the gold concentrations relative to the entire Cordilleran margin, there is a marked tendency for two or more belts or isolated deposits of different ages and genetic types to occur in close proximity within relatively restricted arc (including fore- and back-arc) segments. In the case of the western United States, for example, six belts and four isolated major deposits make up a particularly prominent cluster. If fortuity is discounted, this clustering or pairing of gold concentrations must imply a predisposition of certain arc segments to gold mineralization. An analogous situation is evident for other metals, particularly copper and tin. The reason for the recurrent generation of major deposits and belts dominated by one or more metals remains uncertain, although heterogeneously distributed metal preconcentrations, favorable redox conditions, or other parameters somewhere above the subducted slab, between the mantle wedge and upper crust, are widely contemplated possibilities. Elucidation of the reason(s) for this metallogenic inheritance at the scale of limited arc segments poses an important and challenging series of research questions as well as being critical to the planning of potentially successful greenfield exploration programs.

Estabilidade articular do joelho no quadro do "joelho-flutuante"

Neste trabalho, 22 pacientes com fraturas ipslaterais do fêmur e da tíbia ("joelho flutuante") tratados cirurgicamente foram convocados para reavaliação. Com seguimento mínimo de 4 meses, 17 pacientes compareceram e foram reavaliados através de exame físico, radiológico, escala de Lysholm e o escore de Kärlstron. As fraturas foram classificadas quanto ao grau de exposição (Gustillo e Andersen), cominuição (AO) e o "joelho-flutuante" (Fraser). Doze pacientes (70,6%) apresentaram alterações objetivas no exame físico do joelho. A instabilidade articular foi a alteração mais encontrada, presente em oito casos (47%), seguida da restrição de movimento em sete pacientes (41,2%). A instabilidade anterior foi diagnosticada em cinco casos (29,4%), sendo três associados à instabilidade em varo. A instabilidade posterior estava presente em dois pacientes (11,8%), ambos associados com instabilidade em varo. Um paciente apresentou instabilidade periférica em varo e valgo, associada à restrição importante da flexão do joelho. As presença de fraturas intra-articulares, fraturas expostas do fêmur cursaram com maior incidência de restrição do arco de movimento. Nesta casuística os resultados obtidos reforçam a necessidade da avaliação sistemática da estabilidade articular do joelho, visto que o quadro de "joelho flutuante" está freqüentemente associado à lesão cápsulo-ligamentar desta articulação.

Occult Periarthrosis of the Shoulder

Nineteen outpatients, nine women and ten men, all right-handed, ranging in age from 33 to 87 yrs, with an average age of 53.5 yrs, presented with complaints of lateral epicondylitis (i.e., tennis elbow). Each was subsequently identified as having a heretofore unrecognized loss of ipsilateral shoulder internal rotation. The authors suggest that in this scenario the occult shoulder periarthrosis is interlinked in a pathokinetic chain potentially predisposing to the presenting symptoms of tennis elbow. During a tennis serve, excessive wrist flexion may be substituted as to compensate for a restricted arc of shoulder internal rotation. The extensor carpi radialis longus and brevis cross both the elbow and wrist. Functionally, they have the capacity of reversing their osseous attachments, both at their origin and insertion, as these muscles cycle under load from a concentric/shortening to an eccentric/elongating contraction. Aging muscle, with its increased viscoelastic stiffness, may be "too slow" to accommodate this transition recoil, especially when repetitive. Instead, it is pathomechanically absorbed at the proximal elbow extensor tendon insertion.

Utilization of intestinal clamps for precise cutting of the pectoralis major muscle while raising a myocutaneous flap.

A variety of approaches have been employed for the reconstruction of head and neck defects and most of the techniques involve the use of arterialized vascular flaps alone, or in conjunction with other regional or local tissues. We frequently use a pectoralis major myocutaneous (PMMC) flap in our hospital in addition to other pedicled or free tissue transfers. A PMMC flap is a reliable flap with acceptable complications, needs a small learning curve, takes less time, and does not require additional investment (i.e. microscopes, loops etc). The disadvantages of the PMMC flap is that it has a restricted arc of rotation, gives a cosmetically unacceptable bulk in the neck, it is difficult in females and causes significant shoulder dysfunction. We have made a small improvization in the flap-raising technique which is helpful for the surgeon. This involves utilization of intestinal clamps to hold and cut the pectoralis major muscle.

Intra-oceanic production of continental crust in a Th-depleted ca. 3.0�Ga arc complex, western Superior Province, Canada

The English Lake magmatic complex in the western Superior Province of Canada represents a fragment of early (3.0 Ga) continental crust exposed in oblique cross section through tonalitic upper levels and subjacent quartz diorite, diorite and gabbro, which are cut by late gabbro, anorthosite and hornblendite dykes. Massive, foliated and gneissic units of tonalitic to gab- broic composition, crystallized over a 10 to 18 m.y. period, bear common geochemical attributes, including negative Th, U and Nb anomalies, and only slight LREE and LILE enrichment on NMORB-normalized trace-element profiles. Epsilon Nd values (+0.1 to +1.7) and d 18 O (+6.7 to +8.0 &) do not co-vary with silica or other crustal contamination indices. High Mg#'s and Ni contents suggest derivation from, or interaction with mantle, and large positive anomalies for Ba, Sr and Pb, as well as high U/Th, suggest metaso- matism by hydrous fluids. Trace-element profiles resemble those of primitive intra-oceanic island arc magmas except for the negative Th-U anomaly, which precludes the involvement of either oceanic (sedimentary or basaltic) or continental crust in the petrogenesis of English Lake magmas. In order to account for the unusual geochemical character of the suite, we postulate that water-rich fluids derived from subducted, sea-floor- altered serpentinite provided the flux for melting a depleted mantle wedge. Contemporaneous, proximal high Th/Nb tonalites suggest that the zone of serpenti- nite subduction occurred within a restricted arc segment possibly due to subduction of either: (a) a seamount chain oriented broadly perpendicular to an arc, or (b) a similarly oriented serpentinite-enclosed oceanic fracture zone or fault.

Interpolation with restricted arc length

For given data (ti,y~),i= O,I,',n,O=to<tl <'<t.= 1 we study constrained interpolation problem of Favard type