Robust nonlinear optimization with conic representable uncertainty set

The robust optimization methodology is known as a popular method dealing with optimization problems with uncertain data and hard constraints. This methodology has been applied so far to various convex conic optimization problems where only their inequality constraints are subject to uncertainty. In this paper, the robust optimization methodology is applied to the general nonlinear programming (NLP) problem involving both uncertain inequality and equality constraints. The uncertainty set is defined by conic representable sets, the proposed uncertainty set is general enough to include many uncertainty sets, which have been used in literature, as special cases. The robust counterpart (RC) of the general NLP problem is approximated under this uncertainty set. It is shown that the resulting approximate RC of the general NLP problem is valid in a small neighborhood of the nominal value. Furthermore a rather general class of programming problems is posed that the robust counterparts of its problems can be derived exactly under the proposed uncertainty set. Our results show the applicability of robust optimization to a wider area of real applications and theoretical problems with more general uncertainty sets than those considered so far. The resulting robust counterparts which are traditional optimization problems make it possible to use existing algorithms of mathematical optimization to solve more complicated and general robust optimization problems.     

Development of <Superscript>111</Superscript>In labeled insulin for receptor imaging/therapy

In order to target insulin receptors in various diabetic and insulinoma conditions, human recombinant insulin was successively labeled with [¹¹¹In]-indium chloride after conjugation with freshly prepared cyclic DTPA-dianhydride (ccDTPA). The best results of the conjugation were obtained by addition of 0.5 mL of an insulin pharmaceutical solution (5 mg/mL, in phosphate buffer, pH 8) to a glass tube pre-coated with DTPA-dianhydride (0.01 mg) at 25 °C with continuous mild stirring for 30 minutes. Radio-thin layer chromatography (RTLC), instant thin layer chromatography (ITLC) and high performance liquid chromatography (HPLC) have shown an overall radiochemical purity of higher than 93% at optimized conditions (specific activity = 550–750 MBq/mg, radiochemical yield =81%). The white blood cell labeling capacity of the tracer was determined up to 4 hours at 37 °C. Preliminary in vivo studies in normal rat model was performed to determine the biodistribution of the radiotracer up to 48 hours. It showed a high liver and spleen uptake of the tracer which is consistent with other reported radiolabeled insulins. SPECT images have also shown high liver accumulation of the tracer.     

Preparation and biological evaluation of radiogallium labeled glucagon for SPECT imaging

In this work, recently prepared ⁶⁷Ga-labeled glucagon (⁶⁷Ga-DTPA-GCG) for imaging studies (radiochemical purity >94%; HPLC, S.A. 296–370 GBq/mM) was used in biological studies. The wild-type rat biodistribution results, 2 h post injection, demonstrated high tissue:muscle ratios for target tissues (liver, kidney, heart, spleen, fat intestine stomach and pancreas), 234, 18.45, 7.12, 1.75, 128.7, 4.9, 6.3 and 1.11, respectively. The tracer binding capacity using freshly prepared rat brain homogenate demonstrated significant specific binding of the tracer to neuronal GCG receptors (⁶⁷Ga-DTPA-GCG/⁶⁷Ga:3 and ⁶⁷Ga-DTPA-GCG/⁶⁷GaDTPA:2.2 at 90 min). SPECT images also demonstrated target specific binding of the tracer at 4 h. The data suggests the tracer is accumulated in GCGR rich tissues 2–4 h post injection, suggesting potentials of the tracer for future imaging studies in glocagonoma models.     

Disk level S-matrix elements at eikonal Regge limit

We examine the calculation of the color-ordered disk level S-matrix element of massless scalar vertex operators for the special case that some of the Mandelstam variables for which there are no open string channel in the amplitude, are set to zero. By explicit calculation we show that the string form factors in the 2n-point functions reduce to one at the eikonal Regge limit.     

On non-linear action of multiple M2-branes

A non-linear SO(8)$\mathit{SO}(8)$ invariant BF type Lagrangian for describing the dynamics of N M2-branes in flat spacetime has been proposed recently in the literature which is an extension of the non-abelian DBI action of N   D2-branes. This action includes only terms with even number of the totally antisymmetric tensor MIJK$M^{IJK}$. We argue that the action should contain terms with odd number of MIJL$M^{IJL}$ as well. We modify the action to include them.     

On modified tachyon DBI action

Recently a modification of the tachyon DBI action has been proposed in which the tachyon carries the internal CP matrix σ₁${\sigma }_1$ and σ₂${\sigma }_2$. In this paper, we find the momentum expansion of the disk level S-matrix element of four tachyons and one gauge field in superstring theory and show that the first and second order terms of the expansion are in perfect agreement with the above tachyon DBI action.     

A proposal for M2-brane–anti-M2-brane action

We propose a manifestly SO(8)$\mathit{SO}(8)$ invariant BF type Lagrangian for describing the dynamics of M2-brane–anti-M2-brane system in flat spacetime. When one of the scalars which satisfies a free-scalar equation takes a large expectation value, the M2-brane–anti-M2-brane action reduces to the tachyon DBI action of D2-brane–anti-D2-brane system in flat spacetime.     

Optimization of Phytosterols Dispersion in an Oil/Water Emulsion Using Mixture Design Approach

Major problems related to enrichment of products with phytosterols are high melting temperature, chalky taste and low solubility in water phase. Dispersion of phytosterols in an emulsion was optimized using a mixture design with four components (phytosterols, emulsifier, soy oil, and water). It was found that the particle size of the dispersed phase decreased with the increase in emulsifier concentration. The appearance viscosity was increased with decreasing particle size. The stability of these emulsions could be correlated with the decrease in surface tension and particle size by using oil and emulsifier as components of oil phase.     

Preparation and biodistribution of [67Ga]-DTPA-gonadorelin in normal rats

Gonadorelin was successively labeled with [⁶⁷Ga]-gallium chloride after residulation with freshly prepared cyclic DTPA-dianhydride. The best results of the conjugation were obtained by the addition of 1 mg of a gonadorelin to a glass tube pre-coated with DTPA-dianhydride (0.33 mg) at 25 °C with continuous mild stirring for 1 hour. Radio thin layer chromatography showed an overall radiochemical purity of >90% at optimized conditions after labeling. HPLC showed a radiochemical purity more than 95% (specific activity = 400–450 GBq/M). The stability of the radioconjugate was tested in presence of human serum at 37 °C. Preliminary in vivo studies in normal rats were performed to determine the biodistribution of the conjugate up to 48 hours. The breast and ovaries uptakes were significantly high in first 15-minute post injection which is in agreement with the other reports regarding the presence of specific GnRH receptors. This tracer can be used in detection of GnRH receptor biodistribution in various diseases and malignancies.