Size Formula Research Articles

Minimum risk sequential point estimation of the stress-strength reliability parameter for exponential distribution

In this article, using purely and two-stage sequential procedures, the problem of minimum risk point estimation of the reliability parameter (R) under the stress–strength model, in case the loss function is squared error plus sampling cost, is considered when the random stress (X) and the random strength (Y) are independent and both have exponential distributions with different scale parameters. The exact distribution of the total sample size and explicit formulas for the expected value and mean squared error of the maximum likelihood estimator of the reliability parameter under the stress–strength model are provided under the two-stage sequential procedure. Using the law of large numbers and Monte Carlo integration, the exact distribution of the stopping rule under the purely sequential procedure is approximated. Moreover, it is shown that both proposed sequential procedures are finite and for special cases the exact distribution of stopping times has a degenerate distribution at the initial sample size. The performances of the proposed methodologies are investigated with the help of simulations. Finally, using a real data set, the procedures are clearly illustrated.

Converting a Subset of LTL Formula to Buchi Automata

The translation of LTL formula into equivalent Buchi automata plays an important role in many algorithms for LTL model checking, which consist in obtaining a Buchi automaton that is equivalent to the software system specification and another one that is equivalent to the negation of the property. The intersection of the two Buchi automata is empty if the model satisfies the property. Generating the Buchi automaton corresponding to an LTL formula may, in the worst case, be exponential in the size of the formula, making the model checking effort exponential in the size of the original formula. There is no polynomial solution for checking emptiness of the intersection. That comes from the translation step of LTL formula into finite state models. This makes verification methods hard or even impossible to be implemented in practice. In this paper, we propose a subset of LTL formula which can be converted to Buchi automata whose the size is polynomia.

Converting A Subset of LTL Formula to Buchi Automata

The translation of LTL formula into equivalent Buchi automata plays an important role in many algorithms for LTL model checking, which consist in obtaining a Buchi automaton that is equivalent to the software system specification and another one that is equivalent to the negation of the property. The intersection of the two Buchi automata is empty if the model satisfies the property. Generating the Buchi automaton corresponding to an LTL formula may, in the worst case, be exponential in the size of the formula, making the model checking effort exponential in the size of the original formula. There is no polynomial solution for checking emptiness of the intersection. That comes from the translation step of LTL formula into finite state models. This makes verification methods hard or even impossible to be implemented in practice. In this paper, we propose a subset of LTL formula which can be converted to Buchi automata whose the size is polynomial.

Novel Nanostructured Lipid Carriers with Photoprotective Properties Made from Carnauba Wax, Beeswax, and Kenaf Seed Oil

AbstractThis study was aimed to produce a stable kenaf seed oil‐nanostructured lipid carrier (KSO‐NLC) sunscreen, which can help in the photoprotective effect. The nanostructured lipid carrier (NLC) formulation was optimized and selected based on the results of mean particle size, polydispersity index (PDI), and storage stability of formulas at both chilled (4 ± 2 °C) and room (25 ± 2 °C) temperatures. Uvinul A plus B was added to KSO‐NLC with the optimized formula (80% w/w aqueous phase, 20% w/w lipid phase, and 7% w/w of surfactants with a ratio of 70:15:15 of Tween 20: poloxamer 188: lecithin). The mean particle size distribution (224.73 ± 1.56 nm) and PDI (0.41 ± 0.01) of KSO‐NLC were determined and were found to be stable against storage without creaming or phase separation. The 2,2‐Diphenyl‐1‐picrylhydrazyl (DPPH) radical‐scavenging and 2,2′‐Azino‐bis(3‐ethylbenzothiazoline‐6‐sulfonic acid) diammonium salt (ABTS) radical‐scavenging activities of KSO‐NLC were 5.43 ± 1.00 mg Trolox equiv. g−1 of NLC and 6.70 ± 0.31 mg Trolox equiv. g−1 of NLC, respectively. The Sun Protection Factor (SPF) of KSO‐NLC, 41.38 ± 6.03 with a UVA/UVB ratio 0.64 ± 0.01, suggested a good photoprotective effect. The sustained release of Univul A plus B from KSO‐NLC accompanied by its entrapment efficiency up to 64.09 ± 0.98% and drug loading (DL) of 32.05 ± 0.49% (maximum 50% DL capacity) proved that the degradation of the ultraviolet (UV) filter could be reduced. Therefore, the KSO‐NLC sunscreen was a feasible solution for the photoprotective approach by using unconventional plant seed oil with a significant enhancement (P < 0.05) in many aspects compared to the formula without KSO incorporation.

Separation of AC$^0[\oplus]$ Formulas and Circuits

This paper gives the first separation between the power of {\em formulas} and {\em circuits} of equal depth in the $\mathrm{AC}^0[\oplus]$ basis (unbounded fan-in AND, OR, NOT and MOD$_2$ gates). We show, for all $d(n) \le O(\frac{\log n}{\log\log n})$, that there exist {\em polynomial-size depth-$d$ circuits} that are not equivalent to {\em depth-$d$ formulas of size $n^{o(d)}$} (moreover, this is optimal in that $n^{o(d)}$ cannot be improved to $n^{O(d)}$). This result is obtained by a combination of new lower and upper bounds for {\em Approximate Majorities}, the class of Boolean functions $\{0,1\}^n \to \{0,1\}$ that agree with the Majority function on $3/4$ fraction of inputs. $\mathrm{AC}^0[\oplus]$ formula lower bound: We show that every depth-$d$ $\mathrm{AC}^0[\oplus]$ formula of size $s$ has a {\em $1/8$-error polynomial approximation} over $\mathbb{F}_2$ of degree $O(\frac{1}{d}\log s)^{d-1}$. This strengthens a classic $O(\log s)^{d-1}$ degree approximation for \underline{circuits} due to Razborov. Since the Majority function has approximate degree $\Theta(\sqrt n)$, this result implies an $\exp(\Omega(dn^{1/2(d-1)}))$ lower bound on the depth-$d$ $\mathrm{AC}^0[\oplus]$ formula size of all Approximate Majority functions for all $d(n) \le O(\log n)$. Monotone $\mathrm{AC}^0$ circuit upper bound: For all $d(n) \le O(\frac{\log n}{\log\log n})$, we give a randomized construction of depth-$d$ monotone $\mathrm{AC}^0$ circuits (without NOT or MOD$_2$ gates) of size $\exp(O(n^{1/2(d-1)}))$ that compute an Approximate Majority function. This strengthens a construction of \underline{formulas} of size $\exp(O(dn^{1/2(d-1)}))$ due to Amano.

Novel Combination for Self-Nanoemulsifying Drug Delivery System of Candesartan Cilexetil

Solubility problem of many of effective pharmaceutical molecules are still one of the major obstacle in theformulation of such molecules. Candesartan cilexetil (CC) is angiotensin II receptor antagonist with very low water solubility and this result in low and variable bioavailability. Self- emulsifying drug delivery system (SEDDS) showed promising result in overcoming solubility problem of many drug molecules. CC was prepared as SEDDS by using novel combination of two surfactants (tween 80 and cremophore EL) and tetraglycol as cosurfactant, in addition to the use of triacetin as oil. Different tests were performed in order to confirm the stability of the final product which includes thermodynamic study, determination of self-emulsification time, particle size and zeta potential measurement, and in-vitro drug release. The results showed that the particle size of the best formula was 13.3 nm and zeta potential of -37.45 mV with approximately 100% release after 45 minutes .These results suggest that the preparation of CC. as SEDDS with the use of the above combination of surfactant and cosurfactant is a promising maneuver for oral delivery of CC. in order to improve its bioavailability.

Near exogeneity, weak identification and specification testing: Some asymptotic results

The paper studies the asymptotic size property of various specification tests in linear structural models where instrumental variables may locally violate the exclusion restrictions. Our results provide some new insights and extensions of earlier studies. In particular, we derive an explicit formula of the asymptotic size of the tests which shows clearly the factors that influence their size under instrument endogeneity. We show that all tests have correct asymptotic size when the usual orthogonality condition holds, but their asymptotic size can be arbitrary large even if only one instrument is slightly correlated with the error term. We present a Monte Carlo experiment that confirms our theoretical findings.

On Algebraic Branching Programs of Small Width

In 1979, Valiant showed that the complexity class VP e of families with polynomially bounded formula size is contained in the class VP s of families that have algebraic branching programs (ABPs) of polynomially bounded size. Motivated by the problem of separating these classes, we study the topological closure VP e , i.e., the class of polynomials that can be approximated arbitrarily closely by polynomials in VP e . We describe VP e using the well-known continuant polynomial (in characteristic different from 2). Further understanding this polynomial seems to be a promising route to new formula size lower bounds. Our methods are rooted in the study of ABPs of small constant width. In 1992, Ben-Or and Cleve showed that formula size is polynomially equivalent to width-3 ABP size. We extend their result (in characteristic different from 2) by showing that approximate formula size is polynomially equivalent to approximate width-2 ABP size. This is surprising because in 2011 Allender and Wang gave explicit polynomials that cannot be computed by width-2 ABPs at all! The details of our construction lead to the aforementioned characterization of VP e . As a natural continuation of this work, we prove that the class VPN can be described as the class of families that admit a hypercube summation of polynomially bounded dimension over a product of polynomially many affine linear forms. This gives the first separations of algebraic complexity classes from their nondeterministic analogs.

α-GLUCOSIDASE INHIBITORY ACTIVITY AND FORMULATION OF SOLID LIPID NANOPARTICLE CONTAINING ETHANOL 70% STANDARDIZED EXTRACT OF KUMIS KUCING LEAVES (Orthosiphon stamineus Benth.)

Kumis kucing leaves (Orthosiphon stamineus Benth.) are one type of plants that is able to inhibit the activity of α-glucosidase enzyme. This study aims to formulate Solid Lipid Nanoparticle from ethanol 70% standardized extract of kumis kucing leaves and which give α-glucosidase enzyme inhibitory activity. The result of SLN characteristic for particle size of formula I, II and III shows the result of 51,60 nm; 12.81 nm; 11.87 nm and zeta potential of formula I, II and III show the results -27.67; -10,7; -15.0, respectively. The results of the α-glucosidase enzyme inhibitory activity of the standardized extract, SLN formula I, II and III respectively showed IC50 of 132.9 ppm; 130.3 ppm; 131.4 ppm; 132.2 ppm and Acarbose as comparison showed IC50 of 50.0 ppm. Data processing using t-test statistically at α = 0,05 showed that extract and SLN of formula I had significant difference, thus the best SLN formula was formula I with concentration of tween 80 and propylenglycol of 6% and 10%.

SAT-Based Data Mining

Several propositional satisfiability (SAT) based encodings have been proposed to deal with various data mining problems including itemset and sequence mining problems. This research issue allows to model data mining problems in a declarative way, while exploiting efficient SAT solving techniques. In this paper, we overview our contributions on the application of propositional satisfiability (SAT) to model and solve itemset mining tasks. We first present a SAT based encoding of frequent closed itemset mining task as a propositional formula whose models corresponds to the patterns to be mined. Secondly, we show that some data mining constraints can be avoided by reformulation. We illustrate this issue by reformulating the closeness constraint using the notion of minimal models. Finally, we also addressed the scalability issue, one of the most important challenge of these nice declarative framework. To this end, we proposed a complete partition based approach whose aim is to avoid encoding the whole database as a single formula. Using a partition on the set of items, our new approach leads to several propositional formulas of reasonable size. The experimental evaluation on several known datasets shows huge improvements in comparison to the direct approach without partitioning, while reducing significantly the performance gap with respect to specialized algorithms.

Influence of crosslinker concentration on the characteristics of erythropoietin-alginate microspheres

Context: Microspheres have several advantages including protecting proteins from degradation and clearance after administration and produce a long-term therapeutic effect. Erythropoietin as a neuroprotectant agent has protein-like properties, which are susceptible to degradation and have low in vivo bioavailability. Microspheres formulations is one of potential drug delivery system for erythropoietin. Aims: To evaluate the effect of CaCl2 concentration on the characteristics (particle size, morphology, swelling index, and yield) of erythropoietin-alginate microspheres. Methods: Erythropoietin-alginate microspheres prepared by ionotropic gelation method with aerosolization technique using sodium alginate as polymer and CaCl2 as crosslinker were dried using freeze drying method with maltodextrin as lyoprotectant. The concentrations of alginate used were 2%, and CaCl2 concentrations were 0.5 M(F1), 0.75 M(F2) and 1 M(F3). Results: Results showed smooth and spherical microspheres for all formula with average particle size were 3.23 ± 0.05 μm (F1); 2.99 ± 0.07 μm (F2); and 2.86 ± 0.03 μm (F3). Mass swelling index at 24 h were 1.25 ± 0.10 (F1), 1.18 ± 0.11 (F2), and 1.11 ± 0.10 (F3); at 30 h were 2.00 ± 1.25 (F1), 1.85 ± 0.14 (F2), and 1.72 ± 0.15 (F3) while particle size swelling index at 24 h were 1.15 ± 0.10 (F1), 1.11 ± 0.10 (F2), and 0.97 ± 0.10 (F3); at 30 h were 1.81 ± 0.09 (F1), 1.73 ± 0.15 (F2), and 1.54 ± 0.14 (F3). Respectively yield percentages were 77.76 ± 6.49, 80.01 ± 3.53, and 82.97 ± 4.22. By using One Way ANOVA, it was found that there were significantly differences between three formulas. Conclusions: The particle size of formulas decreased by increasing concentration of CaCl2, whereas no significant difference on swelling index and yield from microspheres with increasing CaCl2 concentration simultaneously.

POWER AND SIZE OF NORMAL DISTRIBUTION AND ITS APPLICATIONS

. The research studied power and size of normal distribution and its applications on linear regression model. The power and size formulas are derived, and the unrestricted test (UT), restrcited test (RT) and pre-test test (PTT) are used. The recommendation of the test is given by choosing maximum power and minimum size, and also graphical analysis. The result showed that the power and size for large standard deviation () tend to be identical and flat. In simulation study, the graphs of the UT, RT, and PTT are still similar to the previous research (Pratikno, 2012), where the PTT tend to lie between UT and RT.

Islamic Knowledge And Attitudes Toward Hiv/Aids Among Undergraduates In UPM Serdang

Research has been conducted attitudes related HIV/AIDS issue particularly among university students because students are the group of younger generation that may be parents advising their children in future or they may have to contact with HIV infected and AIDS people in their future work. The purpose of research design is to identify the most economical method in conducting the research. The non- experimental quantitative research design which is in questionnaire tools has used to finalize results that are based on hypothesis testingThe population of this study is targeted to the undergraduates from Human Ecology in UPM, Serdang. The sample size for the study is determined by the calculation formula (Israel, 2009). The minimum sample size for FEM is approximately 271, which is calculated by the formula of known population size (N = 835) with the 95% confidence level and confidence interval of 5%.to achieve the objectives for this current study. Besides, three techniques of research design are descriptive, correlation and comparative also have been chosen in this study. Descriptive design is used to gather the quantitative information and then organizes, tabulates, depicts, and describes the data collection. Descriptive involved in this study will be given a general description about respondent’s personal characteristic (gender), level of knowledge in HIV/AIDS and attitudes toward HIV/AIDS. The correlation design is applied to determine the linear relationship between personal characteristic (gender), knowledge and attitudes towards HIV/AIDS among FEM undergraduates. The result of the correlation can be positive and negative. If the result is positive correlation, then the changes in value of one variable will make the changes of the other variables in the same direction, or vice versa.

Preparation and Evaluation of Ketoprofen Nanosuspension Using Solvent Evaporation Technique

The effective surface area of drug particle is increased by a reduction in the particle size. Since dissolution takes place at the surface of the solute, the larger the surface area, the further rapid is the rate of drug dissolution. Ketoprofen is class II type drug according to (Biopharmaceutics Classification System BCS) with low solubility and high permeability. The aim of this investigation was to increase the solubility and hence the dissolution rate by the preparation of ketoprofen nanosuspension using solvent evaporation method. Materials like PVP K30, poloxamer 188, HPMC E5, HPMC E15, HPMC E50, Tween 80 were used as stabilizers in perpetration of different formulas of Ketoprofen nanosuspensions. These formulas were evaluated for particle size, entrapment efficiency of drug (EE), effect of stabilizer type, effect of stabilizer concentration and in-vitro dissolution studies. All of the prepared Ketoprofen nanosuspensions formulas showed a particle size result within Nano range. The average particle size of Ketoprofen nanosuspensions formulas was observed from 9.4 nm to 997 nm. Entrapment efficiency was ranged from 79.23% to 95.41 %. The in vitro dissolution studies showed a significant (p<0.01) enhancement in dissolution rate of nanosuspension formulas compared to pure drug (drug alone) and physical mixture (drug and stabilizer). The results indicate the suitability of solvent evaporation method for Ketoprofen with improved in vitro dissolution rate and thus perhaps enhance fast onset of action for drug.

Preparation and Evaluation of Ketoprofen Nanosuspension Using Solvent Evaporation Technique

&#x0D; &#x0D; The effective surface area of drug particle is increased by a reduction in the particle size. Since dissolution takes place at the surface of the solute, the larger the surface area, the further rapid is the rate of drug dissolution. Ketoprofen is class II type drug according to (Biopharmaceutics Classification System BCS) with low solubility and high permeability. The aim of this investigation was to increase the solubility and hence the dissolution rate by the preparation of ketoprofen nanosuspension using solvent evaporation method. Materials like PVP K30, poloxamer 188, HPMC E5, HPMC E15, HPMC E50, Tween 80 were used as stabilizers in perpetration of different formulas of Ketoprofen nanosuspensions. These formulas were evaluated for particle size, entrapment efficiency of drug (EE), effect of stabilizer type, effect of stabilizer concentration and in-vitro dissolution studies. All of the prepared Ketoprofen nanosuspensions formulas showed a particle size result within Nano range. The average particle size of Ketoprofen nanosuspensions formulas was observed from 9.4 nm to 997 nm. Entrapment efficiency was ranged from 79.23% to 95.41 %. The in vitro dissolution studies showed a significant (p&lt;0.01) enhancement in dissolution rate of nanosuspension formulas compared to pure drug (drug alone) and physical mixture (drug and stabilizer). The results indicate the suitability of solvent evaporation method for Ketoprofen with improved in vitro dissolution rate and thus perhaps enhance fast onset of action for drug.

Model and Program Repair via SAT Solving

We consider the subtractive model repair problem : given a finite Kripke structure M and a CTL formula η, determine if M contains a substructure M ′ that satisfies η. Thus, M can be “repaired” to satisfy eta by deleting some transitions and states. We map an instance 〈 M ,η 〉 of model repair to a Boolean formula repair ( M ,η) such that 〈 M ,η 〉 has a solution iff repair ( M ,η) is satisfiable. Furthermore, a satisfying assignment determines which states and transitions must be removed from M to yield a model M ′ of η Thus, we can use any SAT solver to repair Kripke structures. Using a complete SAT solver yields a complete algorithm: it always finds a repair if one exists. We also show that CTL model repair is NP-complete. We extend the basic repair method in three directions: (1) the use of abstraction mappings, that is, repair a structure abstracted from M and then concretize the resulting repair to obtain a repair of M , (2) repair concurrent Kripke structures and concurrent programs: we use the pairwise method of Attie and Emerson to represent and repair the behavior of a concurrent program, as a set of “concurrent Kripke structures”, with only a quadratic increase in the size of the repair formula, and (3) repair hierarchical Kripke structures: we use a CTL formula to summarize the behavior of each “box,” and CTL deduction to relate the box formula with the overall specification.

Succinctness of Order-Invariant Logics on Depth-Bounded Structures

We study the expressive power and succinctness of order-invariant sentences of first-order (FO) and monadic second-order (MSO) logic on structures of bounded tree-depth. Order-invariance is undecidable in general and, thus, one strives for logics with a decidable syntax that have the same expressive power as order-invariant sentences. We show that on structures of bounded tree-depth, order-invariant FO has the same expressive power as FO. Our proof technique allows for a fine-grained analysis of the succinctness of this translation. We show that for every order-invariant FO sentence there exists an FO sentence whose size is elementary in the size of the original sentence, and whose number of quantifier alternations is linear in the tree-depth. We obtain similar results for MSO. It is known that the expressive power of MSO and FO coincide on structures of bounded tree-depth. We provide a translation from MSO to FO and we show that this translation is essentially optimal regarding the formula size. As a further result, we show that order-invariant MSO has the same expressive power as FO with modulo-counting quantifiers on bounded tree-depth structures.

Size-Treewidth Tradeoffs for Circuits Computing the Element Distinctness Function

In this work we study the relationship between size and treewidth of circuits computing variants of the element distinctness function. First, we show that for each n, any circuit of treewidth t computing the element distinctness function δ n : {0, 1} n → {0, 1} must have size at least $\Omega (\frac {n^{2}}{2^{O(t)} \log n})$ . This result provides a non-trivial generalization of a super-linear lower bound for the size of Boolean formulas (treewidth 1) due to Neciporuk. Subsequently, we turn our attention to read-once circuits, which are circuits where each variable labels at most one input vertex. For each n, we show that any read-once circuit of treewidth t and size s computing a variant τ n : {0, 1} n → {0, 1} of the element distinctness function must satisfy the inequality $t\cdot \log s \geq \Omega (\frac {n}{\log n})$ . Using this inequality in conjunction with known results in structural graph theory, we show that for each fixed graph H, read-once circuits computing τ n which exclude H as a minor must have size at least Ω(n 2/log4 n). For certain well studied functions, such as the triangle-freeness function, this last lower bound can be improved to Ω(n 2/log 2n).

Two-dimensional analysis of progressive delamination in thin film electrodes

By employing the two-dimensional analysis, i.e., plane strain and plane stress, a semi-analytical method is developed to investigate the interfacial delamination in electrodes. The key parameters are obtained from the governing equations, and their effects on the evolution of the delamination are evaluated. The impact of constraint perpendicular to the plane is also investigated by comparing the plane strain and plane stress. It is found that the delamination in the plane strain condition occurs easier, indicating that the constraint is harmful to maintain the structure stability. According to the obtained governing equations, a formula of the dimensionless critical size for delamination is provided, which is a function of the maximum volumetric strain and the Poisson’s ratio of the active layer.

Efficient encoding for bounded model checking of timed automata

Bounded model checking (BMC) of timed automata has been successfully applied to verify concurrent real‐time systems, but its scalability is still limited by the large bound required to find counter‐example, the efficiency of the decision procedure which is employed to solve the BMC formula, as well as the large search space for solving satisfiability of the resulting formula. In this paper, we present a systemic encoding scheme to attack all the above three problems. To attack the first problem, we first encode a discrete action followed by a time delay as a composed transition to cut the BMC steps which are used to characterize the time elapse. Then we take advantage of the local time semantics to allow more independent actions to be executed in parallel, which further reduces the required number of BMC steps and hence also the formula size. To employ a more efficient decision procedure, we also translate the linear arithmetic encoding of timed automata to a difference logic formula which can be solved more efficient by a satisfiability modulo theory solver. To address the last problem, we employ explicit‐state partial order reduction idea of only executing some of the enabled transitions to add additional constrains to eliminate some redundant multi‐step executions, thus restricting the search space. Experimental results show that our encoding performs significantly better than previous encodings. © 2017 Institute of Electrical Engineers of Japan. Published by John Wiley &amp; Sons, Inc.