Fractional bioheat equation

In this work we develop a new mathematical model for the Pennes’ bioheat equation assuming a fractional time derivative of single order. A numerical method for the solu- tion of such equations is proposed, and, the suitability of the new model for modelling real physical problems is studied and discussed

Igneous layering, fractional crystallization and growth of granitic plutons: The Dolbel batholith in SW Niger

This study reassesses the development of compositional layering during the growth of granitic plutons, with emphasis on fractional crystallization and its interaction with both injection and inflation-related deformation. The Dolbel batholith (SW Niger) consists of 14, kilometre-sized plutons emplaced by pulsed magma inputs. Each pluton has a coarse-grained core and a peripheral layered series. Rocks consist of albite (An(<= 11)), K-feldspar (Or(96 99), Ab(1) (4)), quartz, edenite (X(Mg)=0337-0.55), augite (X(Mg)=0.65-0.72) and accessories (apatite, titanite and Fe-Ti-oxides). Whole-rock compositions are metaluminous, sodic (K(2)O/Na(2)O=0.49-0.62) and iron-rich [FeO(tot)/(FeO(tot)+MgO)=0.65-0.82]. The layering is present as size-graded and modally graded, sub-vertical, rhythmic units. Each unit is composed of three layers, which are, towards the interior: edenite +/- plagioclase (C(a/p)), edenite+plagioclase+augite+quartz (C(q)), and edenite+plagioclase+augite+quartz+K-feldspar (C(k)). All phases except quartz show zoned microstructures consisting of external intercumulus overgrowths, a central section showing oscillatory zoning and, in the case of amphibole and titanite, complexly zoned cores. Ba and Sr contents of feldspars decrease towards the rims. Plagioclase crystal size distributions are similar in all units, suggesting that each unit experienced a similar thermal history. Edenite, characteristic of the basal C(a/p) layer, is the earliest phase to crystallize. Microtextures and phase diagrams suggest that edenite cores may have been brought up with magma batches at the site of emplacement and mechanically segregated along the crystallized wall, whereas outer zones of the same crystals formed in situ. The subsequent C(q) layers correspond to cotectic compositions in the Qz-Ab-Or phase diagram at P(H2O)=5 kbar. Each rhythmic unit may therefore correspond to a magma batch and their repetition to crystallization of recurrent magma recharges. Microtextures and chemical variations in major phases allow four main crystallization stages to be distinguished: (1) open-system crystallization in a stirred magma during magma emplacement, involving dissolution and overgrowth (core of edenite and titanite crystals); (2) in situ fractional crystallization in boundary layers (C(a/p) and C(q) layers); (3) equilibrium `en masse' eutectic crystallization (C(k) layers); (4) compaction and crystallization of the interstitial liquid in a highly crystallized mush (e. g. feldspar intercumulus overgrowths). It is concluded that the formation of the layered series in the Dolbel plutons corresponds principally to in situ differentiation of successive magma batches. The variable thickness of the Ck layers and the microtextures show that crystallization of a rhythmic unit stops and it is compacted when a new magma batch is injected into the chamber. Therefore, assembly of pulsed magma injections and fractional crystallization are independent, but complementary, processes during pluton construction.

The effects of derivative use on equity fund performance

Investing in mutual funds has become more popular than ever and the amount of money invested in mutual funds registered in Finland has hit its all-time high. Mutual funds provide a relatively low-cost method for private investors to invest in stock market and achieve diversified portfolios. In finance there is always a tradeoff between risk and return, where higher expected returns can usually be achieved only by taking higher risks. Diversifying the portfolio gets rid some of the risk but systematic risk cannot be diversified away. These risks can be managed by hedging the investments with derivatives. The use of derivatives should improve the performance of the portfolios using them compared to the funds that don’t. However, previous studies have shown that the risk exposure and return performance of derivative users does not considerably differ from nonusers. The purpose of this study is to examine how the use of derivatives affects the performance of equity funds. The funds studied were 155 equity funds registered in Finland in 2013. Empirical research was done by studying the derivative use of the funds during a 6-year period between 2008–2013. The performance of the funds was studied quantitatively by using several different performance measures used in mutual fund industry; Sharpe Ratio, Treynor Ratio, Jensen's alpha, Sortino Ratio, M2 and Omega Ratio. The effect of derivative use on funds' performance was studied by using a dummy variable and comparing performance measures of derivative-users and nonusers. The differences in performance measures between the two groups were analyzed with statistical tests. The hypothesis was that funds' derivative use should improve their performance relative to the funds that don't use them. The results of this study are in line with previous studies that state that the use of derivatives does not improve mutual funds' performance. When performance was measured with Jensen's alpha, funds that did not use derivatives performed better than the ones that used them. When measured with other performance measures, the results didn’t differ between two groups.

An LMS style variable tap-length algorithm for structure adaptation

Searching for the optimum tap-length that best balances the complexity and steady-state performance of an adaptive filter has attracted attention recently. Among existing algorithms that can be found in the literature, two of which, namely the segmented filter (SF) and gradient descent (GD) algorithms, are of particular interest as they can search for the optimum tap-length quickly. In this paper, at first, we carefully compare the SF and GD algorithms and show that the two algorithms are equivalent in performance under some constraints, but each has advantages/disadvantages relative to the other. Then, we propose an improved variable tap-length algorithm using the concept of the pseudo fractional tap-length (FT). Updating the tap-length with instantaneous errors in a style similar to that used in the stochastic gradient [or least mean squares (LMS)] algorithm, the proposed FT algorithm not only retains the advantages from both the SF and the GD algorithms but also has significantly less complexity than existing algorithms. Both performance analysis and numerical simulations are given to verify the new proposed algorithm.

Two-branes with variable tension model and the effective Newtonian constant

It is shown that, in the two brane time variation model framework, if the hidden brane tension varies according to the phenomenological Eotvos law, the visible brane tension behavior is such that its time derivative is negative in the past and positive after a specific time of cosmological evolution. This behavior is interpreted in terms of a useful mechanical system analog and its relation with the variation of the Newtonian (effective) gravitational constant is explored.

Fractional polynomial response surface models

Second-order polynomial models have been used extensively to approximate the relationship between a response variable and several continuous factors. However, sometimes polynomial models do not adequately describe the important features of the response surface. This article describes the use of fractional polynomial models. It is shown how the models can be fitted, an appropriate model selected, and inference conducted. Polynomial and fractional polynomial models are fitted to two published datasets, illustrating that sometimes the fractional polynomial can give as good a fit to the data and much more plausible behavior between the design points than the polynomial model. © 2005 American Statistical Association and the International Biometric Society.

A prelude to the fractional calculus applied to tumor dynamic

In order to refine the solution given by the classical logistic equation and extend its range of applications in the study of tumor dynamics, we propose and solve a generalization of this equation, using the so-called Fractional Calculus, i.e., we replace the ordinary derivative of order 1, in one version of the usual equation, by a non-integer derivative of order 0 < α < 1, and recover the classical solution as a particular case. Finally, we analyze the applicability of this model to describe the growth of cancer tumors.

Six-element circuit for maximum power point tracking in photovoltaic-motor systems with variable-frequency drives

A low-cost circuit was developed for stable and efficient maximum power point (MPP) tracking in autonomous photo voltaic-motor systems with variable-frequency drives (VFDs). The circuit is made of two resistors, two capacitors, and two Zener diodes. Its input is the photovoltaic (PV) array voltage and its output feeds the proportional-integral-derivative (PID) controller usually integrated into, the drive. The steady-state frequency-voltage oscillations induced by the circuit were treated in a simplified mathematical model, which was validated by widely characterizing a PV-powered centrifugal pump. General procedures for circuit and controller tuning were recommended based on model equations. The tracking circuit presented here is widely applicable to PV-motor system with VFDs, offering an. efficient open-access technology of unique simplicity. Copyright (C) 2010 John Wiley & Sons, Ltd.

Healing of two and three wall intrabony periodontal defects following treatment with an enamel matrix derivative combined with autogenous bone

BACKGROUND: There are still limited data on the outcomes of regenerative periodontal surgery using a combination of an enamel matrix protein derivative (EMD) and autogenous bone (AB). AIM: To evaluate the healing of deep intrabony defects treated with either a combination EMD+AB or EMD alone. MATERIALS AND METHODS: Forty patients with advanced chronic periodontitis, with one deep intrabony defect, were randomly treated with either EMD+AB (test) or EMD (control). Clinical assessments were performed at baseline and at 1 year after treatment. The primary outcome variable was relative attachment level (RAL). RESULTS: Healing was uneventful in all patients. The test sites showed a reduction in the mean probing pocket depth (PPD) of 5.6 +/- 0.9 mm (p<0.001), a gain in the mean RAL of 4.2 +/- 1.1 mm (p<0.001) and a gain in the mean probing bone level (PBL) of 3.9 +/- 1.0 mm (p<0.001). The control group displayed a mean PPD reduction of 4.6 +/- 0.4 mm (p<0.001), a mean RAL gain of 3.4 +/- 0.8 mm (p<0.001) and a mean PBL gain of 2.8 +/- 0.8 mm (p<0.001). RAL gains of > or =4 mm were measured in 90% of the test defects and in 55% of the controls. PBL gains of > or =4 mm were obtained in 85% of the test defects and in 25% of the control ones. The test treatment resulted in statistically higher PPD reductions, RAL gains and PBL gains compared with the control (p<0.01). CONCLUSIONS: Within their limits, the present results indicate that: (i) at 1 year after surgery, both therapies resulted in statistically significant clinical improvements compared with baseline and (ii) although the combination of EMD+AB resulted in statistically significant higher soft and hard tissue improvements compared with treatment with EMD, the clinical relevance of this finding is unclear.

Four-year results following treatment of intrabony periodontal defects with an enamel matrix derivative alone or combined with a biphasic calcium phosphate

The aim of this study was to evaluate the 4-year clinical outcomes following regenerative surgery in intrabony defects with either EMD + BCP or EMD. Twenty-four patients with advanced chronic periodontitis, displaying one-, two-, or three-walled intrabony defect with a probing depth of at least 6 mm, were randomly treated with either EMD + BCP (test) or EMD alone (control). The following clinical parameters were evaluated at baseline, at 1 year and at 4 years after regenerative surgery: plaque index, gingival index, bleeding on probing, probing depth, gingival recession, and clinical attachment level (CAL). The primary outcome variable was CAL. No differences in any of the investigated parameters were observed at baseline between the two groups. The test group demonstrated a mean CAL change from from 10.8 ± 1.6 mm to 7.4 ± 1.6 mm (p < 0.001) and to 7.6 ± 1.7 mm (p < 0.001) at 1 and 4 years, respectively. In the control group, mean CAL changed from 10.4 ± 1.3 at baseline to 6.9 ± 1.0 mm (p < 0.001) at 1 year and 7.2 ± 1.2 mm (p < 0.001) at 4 years. At 4 years, two defects in the test group and three defects in the control group have lost 1 mm of the CAL gained at 1 year. Compared to baseline, at 4 years, a CAL gain of ≥3 mm was measured in 67% of the defects (i.e., in 8 out of 12) in the test group and in 75% of the defects (i.e., in 9 out of 12) in the control group. There were no statistically significant differences in any of the investigated parameters at 1 and at 4 years between the two groups. Within their limits, the present results indicate that: (a) the clinical improvements obtained with both treatments can be maintained over a period of 4 years, and (b) in two- and three-walled intrabony defects, the addition of BCP did not additionally improve the outcomes obtained with EMD alone. In two- and three-walled intrabony defects, the combination of EMD + BCP did not show any advantage over the use of EMD alone.

Influence of enamel matrix derivative on cells at different maturation stages of differentiation

Enamel matrix derivative (EMD), a porcine extract harvested from developing porcine teeth, has been shown to promote formation of new cementum, periodontal ligament and alveolar bone. Despite its widespread use, an incredibly large variability among in vitro studies has been observed. The aim of the present study was to determine the influence of EMD on cells at different maturation stages of osteoblast differentiation by testing 6 cell types to determine if cell phenotype plays a role in cell behaviour following treatment with EMD. Six cell types including MC3T3-E1 pre-osteoblasts, rat calvarial osteoblasts, human periodontal ligament (PDL) cells, ROS cells, MG63 cells and human alveolar osteoblasts were cultured in the presence or absence of EMD and proliferation rates were quantified by an MTS assay. Gene expression of collagen1(COL1), alkaline phosphate(ALP) and osteocalcin(OC) were investigated by real-time PCR. While EMD significantly increased cell proliferation of all cell types, its effect on osteoblast differentiation was more variable. EMD significantly up-regulated gene expression of COL1, ALP and OC in cells early in their differentiation process when compared to osteoblasts at later stages of maturation. Furthermore, the effect of cell passaging of primary human PDL cells (passage 2 to 15) was tested in response to treatment with EMD. EMD significantly increased cell proliferation and differentiation of cells at passages 2-5 however had completely lost their ability to respond to EMD by passages 10+. The results from the present study suggest that cell stimulation with EMD has a more pronounced effect on cells earlier in their differentiation process and may partially explain why treatment with EMD primarily favors regeneration of periodontal defects (where the periodontal ligament contains a higher number of undifferentiated progenitor cells) over regeneration of pure alveolar bone defects containing no periodontal ligament and a more limited number of osteoprogenitor cells.

Five-year results evaluating the effects of platelet-rich plasma on the healing of intrabony defects treated with enamel matrix derivative and natural bone mineral

BACKGROUND Regenerative periodontal surgery using the combination of enamel matrix derivative (EMD) and natural bone mineral (NBM) with and without addition of platelet-rich plasma (PRP) has been shown to result in substantial clinical improvements, but the long-term effects of this combination are unknown. METHODS The goal of this study was to evaluate the long-term (5-year) outcomes after regenerative surgery of deep intrabony defects with either EMD + NBM + PRP or EMD + NBM. Twenty-four patients were included. In each patient, one intrabony defect was randomly treated with either EMD + NBM + PRP or EMD + NBM. Clinical parameters were evaluated at baseline and 1 and 5 years after treatment. The primary outcome variable was clinical attachment level (CAL). RESULTS The sites treated with EMD + NBM + PRP demonstrated a mean CAL change from 10.5 ± 1.6 to 6.0 ± 1.7 mm (P <0.001) at 1 year and 6.2 ± 1.5 mm (P <0.001) at 5 years. EMD + NBM-treated defects showed a mean CAL change from 10.6 ± 1.7 to 6.1 ± 1.5 mm (P <0.001) at 1 year and 6.3 ± 1.4 mm (P <0.001) at 5 years. At 1 year, a CAL gain of ≥4 mm was measured in 83% (10 of 12) of the defects treated with EMD + NBM + PRP and in 100% (all 12) of the defects treated with EMD + NBM. Compared to baseline, in both groups at 5 years, a CAL gain of ≥4 mm was measured in 75% (nine of 12 in each group) of the defects. Four sites in the EMD + PRP + NBM group lost 1 mm of the CAL gained at 1 year. In the EMD + NBM group, one defect lost 2 mm and four other defects lost 1 mm of the CAL gained at 1 year. No statistically significant differences in any of the investigated parameters were observed between the two groups. CONCLUSIONS Within their limits, the present results indicate that: 1) the clinical outcomes obtained with both treatments can be maintained up to a period of 5 years; and 2) the use of PRP does not appear to improve the results obtained with EMD + NBM.

Ten-year results following treatment of intrabony defects with an enamel matrix protein derivative combined with either a natural bone mineral or a β-tricalcium phosphate

BACKGROUND The purpose of the present study is to evaluate the 10-year results following treatment of intrabony defects treated with an enamel matrix protein derivative (EMD) combined with either a natural bone mineral (NBM) or β-tricalcium phosphate (β-TCP). METHODS Twenty-two patients with advanced chronic periodontitis and displaying one deep intrabony defect were randomly treated with a combination of either EMD + NBM or EMD + β-TCP. Clinical evaluations were performed at baseline and at 1 and 10 years. The following parameters were evaluated: plaque index, bleeding on probing, probing depth, gingival recession, and clinical attachment level (CAL). The primary outcome variable was CAL. RESULTS The defects treated with EMD + NBM demonstrated a mean CAL change from 8.9 ± 1.5 mm to 5.3 ± 0.9 mm (P <0.001) and to 5.8 ± 1.1 mm (P <0.001) at 1 and 10 years, respectively. The sites treated with EMD + β-TCP showed a mean CAL change from 9.1 ± 1.6 mm to 5.4 ± 1.1 mm (P <0.001) at 1 year and 6.1 ± 1.4 mm (P <0.001) at 10 years. At 10 years two defects in the EMD + NBM group had lost 2 mm, whereas two other defects had lost 1 mm of the CAL gained at 1 year. In the EMD + β-TCP group three defects had lost 2 mm, whereas two other defects had lost 1 mm of the CAL gained at 1 year. Compared with baseline, at 10 years, a CAL gain of ≥3 mm was measured in 64% (i.e., seven of 11) of the defects in the EMD + NBM group and in 82% (i.e., nine of 11) of the defects in the EMD + β-TCP group. No statistically significant differences were found between the 1- and 10-year values in either of the two groups. Between the treatment groups, no statistically significant differences in any of the investigated parameters were observed at 1 and 10 years. CONCLUSION Within their limitations, the present findings indicate that the clinical improvements obtained with regenerative surgery using EMD + NBM or EMD + β-TCP can be maintained over a period of 10 years.

The modified coronally advanced tunnel combined with an enamel matrix derivative and subepithelial connective tissue graft for the treatment of isolated mandibular Miller Class I and II gingival recessions: a report of 16 cases.

OBJECTIVES To clinically evaluate the healing of mandibular Miller Class I and II isolated gingival recessions treated with the modified coronally advanced tunnel (MCAT) in conjunction with an enamel matrix derivative (EMD) and subepithelial connective tissue graft (SCTG). METHOD AND MATERIALS Sixteen healthy patients (13 women and 3 men) exhibiting one isolated mandibular Miller Class I and II gingival recessions of a depth of ≥ 3 mm, were consecutively treated with the MCAT in conjunction with EMD and SCTG. Treatment outcomes were assessed at baseline and at 12 months postoperatively. The primary outcome variable was complete root coverage (CRC) (eg, 100% root coverage). RESULTS Postoperative pain and discomfort were low and no complications such as postoperative bleeding, allergic reactions, abscesses, or loss of SCTG were observed. At 12 months, statistically significant (P < .0001) root coverage was obtained in all 16 defects. CRC was measured in 12 out of the 16 cases (75%) while in the remaining 4 defects root coverage amounted to 90% (in two cases) and 80% (in two cases), respectively. Mean root coverage was 96.25%. Mean keratinized tissue width increased from 1.98 ± 0.8 mm at baseline to 2.5 ± 0.9 mm (P < .0001) at 12 months, while mean probing depth did not show any statistically significant changes (ie, 1.9 ± 0.3 mm at baseline vs 1.8 ± 0.2 mm at 12 months). CONCLUSION Within their limits, the present results indicate that the described treatment approach may lead to predictable root coverage of isolated mandibular Miller Class I and II gingival recessions.

Clinical outcomes following regenerative therapy of non-contained intrabony defects using a deproteinized bovine bone mineral combined with either enamel matrix derivative or collagen membrane

BACKGROUND The purpose of this study is to compare clinical outcomes in the treatment of deep non-contained intrabony defects (i.e., with ≥70% 1-wall component and a residual 2- to 3-wall component in the most apical part) using deproteinized bovine bone mineral (DBBM) combined with either enamel matrix protein derivative (EMD) or collagen membrane (CM). METHODS Forty patients with multiple intrabony defects were enrolled. Only one non-contained defect per patient with an intrabony depth ≥3 mm located in the interproximal area of single- and multirooted teeth was randomly assigned to the treatment with either EMD + DBBM (test: n = 20) or CM + DBBM (control: n = 20). At baseline and after 12 months, clinical parameters including probing depth (PD) and clinical attachment level (CAL) were recorded. The primary outcome variable was the change in CAL between baseline and 12 months. RESULTS At baseline, the intrabony component of the defects amounted to 6.1 ± 1.9 mm for EMD + DBBM and 6.0 ± 1.9 mm for CM + DBBM sites (P = 0.81). The mean CAL gain at sites treated with EMD + DBBM was not statistically significantly different (P = 0.82) compared with CM + DBBM (3.8 ± 1.5 versus 3.7 ± 1.2 mm). No statistically significant difference (P = 0.62) was observed comparing the frequency of CAL gain ≥4 mm between EMD + DBBM (60%) and CM + DBBM (50%) or comparing the frequency of residual PD ≥6 mm between EMD + DBBM (5%) and CM + DBBM (15%) (P = 0.21). CONCLUSION Within the limitations of the present study, regenerative therapy using either EMD + DBBM or CM + DBBM yielded comparable clinical outcomes in deep non-contained intrabony defects after 12 months.