Free Endpoint Research Articles

DYNAMIC SYSTEM OF TUBERCULOSIS MODEL USING OPTIMAL CONTROL IN SEMARANG CITY INDONESIA

Tuberculosis is a disease which is very contagious among human. To prevent this from happening, Semarang city government has enacted vaccination for exposed individuals and treatment for the infected individuals. Vaccination and treatment are forms of control that will be applied to dynamic model systems of Tuberculosis. The present paper will describe epidemic model of Tuberculosis with control using Pontryagin Minimum Principle to find optimal solution of the control with fixed time and free end point. The optimal control will aim to reduce or minimize the number of infected populations. Numerical calculation is carried out with MATLAB software programming to illustrate and compare the graph of the dynamic model with and without optimal control. The results of dynamic modeling of Tuberculosis with control state that vaccination and treatment have succeeded in reducing the population of infected individuals.

Invasive Nodal Staging via Endobronchial Ultrasound and Outcome in Patients Treated with Stereotactic Body Radiation Therapy for Early-Stage Non-Small Cell Lung Cancer – Results from a Single Institution Study

IntroductionStereotactic body radiation therapy (SBRT) is an effective treatment for medically inoperable early-stage non-small cell lung cancer (NSCLC). The prognostic value of invasive nodal staging (INS) for patients undergoing SRBT has not been studied extensively. Herein, we report the impact of INS in addition to 18F-FDG-PET on treatment outcome for patients with NSCLC undergoing SBRT. Materials and MethodsPatients with stage I/ II NSCLC who underwent SBRT were included with IRB approval. Clinical, dosimetric, and radiological data were obtained. Overall survival (OS), regional recurrence free survival (RRFS), local recurrence free survival (LRFS), and distant recurrence free survival (DRFS) were analyzed using Kaplan Meyer method. Univariable analysis (UVA) and multivariable analysis (MVA) were performed to assess the relationship between the variables and the outcomes. ResultsA total of 376 patients were included in the analysis. Median follow up was 43 months (IQ 32.6-45.8). Median OS, LRFS, RRFS, DRFS were 40, 32, 32, 33 months, respectively. The 5-year local, regional, and distant failure rates were 13.4%, 23.5% and 25.3%, respectively. The 1-year, 3-year and 5-year OS were 83.8%, 55.6%, and 36.3%, respectively. On MVA, INS was not a predictor of either improved overall or any recurrence free survival endpoints while larger tumor size, age, and adjusted Charleston co-morbidity index (aCCI) were significant for inferior LRFS, RRFS, and DRFS. ConclusionInvasive nodal staging did not improve overall or recurrence free survival among patients with early-stage NSCLC treated with SBRT whereas older age, aCCI, and larger tumor size were significant predictors of LRFS, RRFS, and DRFS.

Statistical analysis of coupled oscillations with a single fixed endpoint and its application to carbon nanomaterials

Squared deviations from the equilibrium positions of one-dimensional coupled harmonic oscillators with fixed and free endpoints are calculated, and the time averages are expressed as a function of the initial displacements and velocities. Furthermore, we consider the averages of squared deviations over an ensemble of initial displacements and velocities, which distribute based on a product of the same distribution functions with variances of the initial coordinates σx2 and velocities σv2 , respectively. We demonstrate that the mean squared deviation linearly increases as the oscillator separates further from the fixed endpoint because of the asymmetrical boundary conditions, and that the increase rate depends only on σv2 and not on σx2 . This simple statistical property of harmonic oscillation is similarly observed in the oscillations of a graphene sheet and carbon nanotube in molecular dynamics simulations, in which the interacting forces are nonlinear.

A New Optimization Approach for the Tallest Column Design

Motivated by the classical brachistochrone we present a new pattern of finding the shape of a vertical column that attains the maximum height if its material and volume are prescribed. It comprises the optimal control problem with a free end point. Besides, the constitutive equation of the column is such that it can suffer flexure, compression and shear. The critical load of a heavy compressed column for the finite values of shear and extensional rigidity and the novel use of the Pontryagin maximum principle with the corresponding first integral yielding the non-vanishing optimal cross section as a solution of a quadratic equation are main novelties of this work. The classical solution for the tallest column under selfweight is covered as a special case for infinite values of shear and extensional rigidity.

Critical behaviour of the extended-ballistic transition for pulled self-avoiding walks

In order to study long chain polymers many lattice models accommodate a pulling force applied to a particular part of the chain, often a free endpoint. This is in addition to well-studied features such as energetic interaction between the lattice polymer and a surface. However, the critical behaviour of the pulling force alone is less well studied, such as characterising the nature of the phase transition and particularly the values of the associated exponents. We investigate a simple model of lattice polymers subject to forced extension, namely self-avoiding walks (SAWs) on the square and simple cubic lattices with one endpoint attached to an impermeable surface and a force applied to the other endpoint acting perpendicular to the surface. In the thermodynamic limit the system undergoes a transition to a ballistic phase as the force is varied and it is known that this transition occurs whenever the magnitude of the force is positive, i.e. f>fc=0. Using well established scaling arguments we show that the crossover exponent ϕ for the finite-size model is identical to the well-known exponent νd, which controls the scaling of the size of the polymer in d-dimensions. With extensive Monte Carlo simulations we test this conjecture and show that the value of ϕ is indeed consistent with the known values of ν2=3/4 and ν3=0.587597(7). Scaling arguments, in turn, imply the specific heat exponent α is 2/3 in two dimensions and 0.29815(2) in three dimensions.

Evaluation of immunotherapy response score (IRS) for predicting pembrolizumab (pembro) clinical benefit in patients (pts) with advanced solid tumors.

e14646 Background: IRS is a multivariable biomarker algorithm combining tissue-based tumor mutation burden (TMB) with quantitative gene expression biomarkers, previously validated to predict anti-PD-1 and anti-PD-L1 monotherapy (mono) benefit in an observational clinical trial (PMID: 36750617). Herein, we evaluated IRS in pts with advanced solid tumors across the Kaiser Permanente Northern California (KPNC) health system following a pre-specified statistical analysis plan. Methods: KPNC pts with valid IRS results (from 2018 – 2022; specimen collection years 2011-2021) and electronic health record (EHR) documented > 1st line systemic pembro mono treatment were included; pts with gliomas or previous immunotherapy were excluded. All oncologic treatments were obtained from the EHR and standardized to determine time to next treatment (TTNT) as a real-world progression free survival endpoint. A within-pt evaluation was performed, comparing pembro TTNT to the pt’s immediate prior therapy line (prior) TTNT. The primary objective was to determine if IRS status (-H vs. Low [-L]) predicts pembro clinical benefit in Cox proportional hazards models through testing for interaction between IRS status and pembro/prior therapy TTNT. Results: With a data cutoff of 06/15/2022, 211 KPNC pts (142 2nd line and 69 > 2nd line pembro) were eligible and included (from 24 solid tumor types). The median (m) pembro follow-up was 16.0 months. IRS-H pts (n = 77, 36%) had significantly longer pembro vs. prior TTNT (mTTNT 20.3 mo vs. 4.5 mo, log-rank p-value < 0.0001), whereas IRS-L pts (n = 134, 64%) did not (mTTNT 3.3 mo vs. 5.2 mo, log-rank p-value 0.75); the interaction between IRS status and pembro/prior treatment was significant (interaction test p-value < 0.0001). Conclusions: IRS predicted pan-solid tumor pembro mono benefit compared to prior therapy and may be a potential marker for pembro mono treatment decisions. Clinical trial information: NCT03061305 .

The heterogeneous helicoseir

We study the rotations of a heavy string (helicoseir) about a vertical axis with one free endpoint and with arbitrary density, under the action of the gravitational force. We show that the problem can be transformed into a nonlinear eigenvalue equation, as in the uniform case. The eigenmodes of this equation represent equilibrium configurations of the rotating string in which the shape of the string does not change with time. As previously proved by Kolodner for the homogeneous case, the occurrence of new modes of the nonlinear equation is tied to the spectrum of the corresponding linear equation. We have been able to generalize this result to a class of densities ρ(s)=γ(1−s)γ−1, which includes the homogeneous string as a special case (γ=1).We also show that the solutions to the nonlinear eigenvalue equation (NLE) for an arbitrary density are orthogonal and that a solution of this equation with a given number of nodes contains solutions of a different helicoseir, with a smaller number of nodes. Both properties hold also for the homogeneous case and had not been established before.

793P NeoPeLe: A phase II trial of neoadjuvant (NAT) pembrolizumab (Pembro) combined with lenvatinib (Lenva) in resectable stage III melanoma

Neoadjuvant anti-PD-1 (PD1) induces a pathological complete response (pCR) in 20% and any pathological response (pRR) in 34% of stage III pts, with durable survival in responders. Improvements are needed to overcome primary resistance. NeoPele sought to determine if additional clinical benefit can be achieved by adding lenva to pembro using the NAT platform in pts with stage III melanoma (NCT04207086). 20 pts with resectable, RECIST measurable stage III nodal melanoma received 6 wks of NAT with pembro (200mg, IV, Q3W) and lenva (20mg, po, od), then a lymph node dissection (LND), then 46 wks pembro. CT + PET scans were performed at baseline and wk 6; CT was continued 12 wkly to 2 yrs. Primary endpoint was pCR and pRR at wk 6. Secondary endpoints; RECIST RR at wk 6, event-free survival (EFS), relapse free survival (RFS), OS, toxicity and translational endpoints. At data cut off 31 Mar 2022, 20 pts analysed: 30% female, med age 64.7 yrs, 3 (15%) BRAF V600E, 8 (40%) NRAS, 10 (50%) clinical N1b. Med f/u was 11.2 months (95% CI 10.2 - 13.8). 8/20 (40%) pts had pCR and 15/20 (75%) had any path response (Table). Events occurred in 4 pts; 1 had brain metastasis prior to LND with pPR, and 3 post surgery with pNR. Most common toxicities were fatigue (9, 45%), hypertension (8, 40%), headache (6, 30%) and anorexia (5, 25%) due to lenva; 45% were gd 3/4, most commonly hypertension (5, 25%). Most common surgical events were seroma (4, 20%) and lymphoedema (7, 35%), with no DVTs. 4 pts interrupted lenva and 0 permanently discontinued during NAT. Post NAT surgical operability was the same or improved in 13 (65%) pts, and harder in 7 (35%). Longitudinal analysis of melanoma tissue, microenvironment and microbiome is ongoing.Table: 793PPembro+Lenva (n=20)pRR pCR Near pCR pPR pNR15 (75%) 8 (40%) 3 (15%) 4 (20%) 5 (25%)RECIST ORR/CR35% / 5%No. Events4 (20%)No. Recurred/Progressed by pCR/near-pCR/pPR/pNR0/0/1ˆ/3No. Death11-yr EFS (95% CI)80% (95% CI 64-99%)ˆ1 pt progressed in brain prior to surgery but had LND. Open table in a new tab ˆ1 pt progressed in brain prior to surgery but had LND. A high pCR and pRR rate was observed with NAT pembro+lenva, higher than previous studies of PD1 alone. The trial and translational investigations are ongoing, and RFS and OS data will be collected.

Necessary conditions for optimal control problems with sweeping systems and end point constraints

We generalize the Maximum Principle for free end point optimal control problems involving sweeping systems derived in [de Pinho MdR, Ferreira MMA, Smirnov GV. Optimal control involving sweeping processes. Set-Valued Var Anal. 2019;27(2):523–548] to cover the case where the constraints are time dependent and the end point is constrained to a set. As in [de Pinho MdR, Ferreira MMA, Smirnov GV. Optimal control involving sweeping processes. Set-Valued Var Anal. 2019;27(2):523–548], an ingenious smooth approximating family of standard differential equations plays a crucial role.

Multi-phase trajectory optimization of aerospace vehicle using sequential penalized convex relaxation

This paper presents a novel methodology for solving the multi-phase trajectories of aerospace vehicles in the framework of convex optimization. As a result of the inherent non-smooth, non-linear, and staged features of the problem, the application of convex optimization is confronted by three categories of tough non-convex terms, non-convex functions, phase linkage constraints, and free endpoints. To overcome these difficulties, a combination of a time-projection approach, and a sequential relaxation and penalization method is developed in this paper. Firstly, free singularity points from linkage constraints and endpoints are eliminated by projecting the time history onto a normalized time interval. Subsequently, the resulting fixed-time problem is equivalently converted in to a pre-semi-definite form and sequentially relaxed as an approximated convex optimization problem. Furthermore, to increase the convergence of the proposed method, a penalization term is included to control the search direction toward the true solution. Analyses are performed to ensure that the convergence and robustness of the proposed algorithm is well guaranteed. A numerical comparison of the results with those from the state-of-art pseudo-spectral nonlinear programming solver GPOPS suggests that the algorithm outputs similar trajectories, but in only one tenth of the computation time.

Longitudinal oscillations of relaxating rod with free endpoints

Longitudinal oscillations of relaxating rod with free endpoints.

Outcome of patients with recurrent/refractory osteosarcoma enrolled in three recent phase II trials: A report from the Children’s Oncology Group.

11530 Background: Based on seven prior Phase 2 Children’s Oncology Group (COG) trials, the 4-month event-free survival(EFS) and associated confidence interval for relapsed osteosarcoma with measurable disease according to RECIST was determined to be 12% (95% CI 6 - 19%). Three prospective clinical trials were conducted using this historical benchmark to detect activity defined by an EFS improvement of double the upper confidence interval. This report summarizes the outcome of these studies, describes whether the historical data remains an accurate baseline, and considers implications for future phase II trial study design in relapsed osteosarcoma measurable according to RECIST. Methods: We conducted an analysis of outcome for patients with recurrent/refractory osteosarcoma enrolled in three recent prospective COG phase II trials; AOST1321 (unresected cohort), AOST1322 and AOST1521 that used EFS at 4 months as the primary endpoint. Patients were eligible if they had osteosarcoma that had recurred or become refractory after standard therapy and had measurable disease according to RECIST. We assessed whether risk of an EFS event is modified by age, sex, race/ethnicity, number of prior chemotherapy regimens, or time to first relapse. Results: In each of the three phase II trials (unresected group of AOST1321, AOST1322, AOST1521), the drugs tested (denosumab, eribulin and glembatumumab) were concluded to be not effective due to a failure of the patient populations to meet the prespecified active 4-month progression free survival endpoint. The 4-month EFS for the 57 evaluable patients enrolled on these trials was 7% (95% CI 2 – 16%), similar to the 4-month EFS for 96 patients in the previous seven phase II trials of 12% (95% CI 6 - 19%). The combined EFS at 4 months for all 10 studies is 10% (95% CI 6 – 15%).There was no significant difference in EFS across trials based on age, sex, ethnicity, number of prior treatment regimens, consistent with prior analysis. Data from AOST1321 and AOST1521 were analyzed to determine the impact of time to first recurrence on EFS. Two different quantifications were applied: 1 year or less versus 2 or more years; and 2 years or less versus 3 years or more. Neither categorization was statistically significant. Conclusions: The EFS at 4 months in the three new phase II trials is similar to the previous seven phase II single arm trials. The combined analysis of 153 patients from 10 trials tightens the confidence interval, moving the upper 95% CI to 15%. Modification to future study designs could be considered based on this updated analysis. EFS at 4 months remains a robust primary endpoint. Single-arm trials using this endpoint based on the historical benchmark have accrued rapidly and allowed assessment of multiple novel agents in osteosarcoma. The negative trial results and continued poor outcome highlight the need for new approaches for relapsed osteosarcoma. Clinical trial information: NCT02097238, NCT02470091, NCT02487979.

New Variational Problems with an Action Depending on Generalized Fractional Derivatives, the Free Endpoint Conditions, and a Real Parameter

This work presents optimality conditions for several fractional variational problems where the Lagrange function depends on fractional order operators, the initial and final state values, and a free parameter. The fractional derivatives considered in this paper are the Riemann–Liouville and the Caputo derivatives with respect to an arbitrary kernel. The new variational problems studied here are generalizations of several types of variational problems, and therefore, our results generalize well-known results from the fractional calculus of variations. Namely, we prove conditions useful to determine the optimal orders of the fractional derivatives and necessary optimality conditions involving time delays and arbitrary real positive fractional orders. Sufficient conditions for such problems are also studied. Illustrative examples are provided.

Divergent series and the mixed problem for the wave equation with free endpoints

Divergent series and the mixed problem for the wave equation with free endpoints

CTIM-10. PHASE II STUDY OF PEMBROLIZUMAB PLUS SurVaxM FOR GLIOBLASTOMA AT FIRST RECURRENCE

Abstract BACKGROUND Pembrolizumab is a potent humanized immunoglobulin G4 monoclonal antibody with high specificity of binding to the programmed cell death 1 (PD-1) receptor, thus inhibiting its interaction with programmed cell death ligand 2 (PD-L2). Survivin is a 16.5 kDa intracellular protein that belongs to the inhibitor of apoptosis protein (IAP) family. It acts in concert with the mitotic spindle apparatus to regulate cell division and localizes to the spindle microtubule organizing center (MTOC) during the G2/M phase of cell cycle progression. Survivin has also been shown to modulate the function of a number of terminal effector cell death proteases (caspases) leading to an inhibition of apoptosis. METHODS This is a Phase II study of two arms in patients with recurrent glioblastoma. Arm A is patients with first recurrence of glioblastoma who have failed prior chemotherapy and radiation but have not received any immunotherapy. Arm B is an exploratory arm of 10 patients who have failed prior anti-PD1 therapy. The ongoing study is a phase II clinical study with a 10 patient, toxicity run-in. All patients will receive the study drug combination consisting of SurVaxM and pembrolizumab with no randomization, stratification or dose escalation. RESULTS So far ten patients have been enrolled on the study as safety run in. Primary endpoint is Progression free survival at 6 months. Safety and tolerability of Pembrolizumab and SurVaxM, Response rates of Pembrolizumab and SurVaxM determined using RANO criteria are secondary endpoints. Additional secondary endpoints include Overall survival and Progression Free survival Exploratory endpoints include Cellular and humoral immune responses during concurrent administration of Pembrolizumab and SurVaxM. CONCLUSION This is an ongoing clinical trial.

Fractional variational principle of Herglotz for a new class of problems with dependence on the boundaries and a real parameter

The fractional variational problem of Herglotz type for the case where the Lagrangian depends on generalized fractional derivatives, the free endpoints conditions, and a real parameter is studied. This type of problem generalizes several problems recently studied in the literature. Moreover, it allows us to unify conservative and non-conservative dynamical processes in the same model. The dependence of the Lagrangian with respect to the boundaries and a free parameter is effective and transforms the standard Herglotz’s variational problem into a problem of a different nature.

Sufficiency for Purely Essentially Bounded Optimal Controls

For optimal control problems of Bolza with variable and free end-points, nonlinear dynamics, nonlinear isoperimetric inequality and equality restrictions, and nonlinear pointwise mixed time-state-control inequality and equality constraints, sufficient conditions for strong minima are derived. The algorithm used to prove the main theorem of the paper includes a crucial symmetric inequality, making this technique an independent self-contained method of classical concepts such as embedding theorems from ordinary differential equations, Mayer fields, Riccati equations, or Hamilton–Jacobi theory. Moreover, the sufficiency theory given in this article is able to detect discontinuous solutions, that is, solutions which need to be neither continuous nor piecewise continuous but only essentially bounded.

Second-Order Optimality Conditions for Multiobjective Optimal Control Problems with Mixed Pointwise Constraints and Free Right End Point

In this paper, we derive first- and second-order necessary optimality conditions of Karush--Kuhn--Tucker type for H-locally weak solutions in the sense of Pareto of multiobjective optimal control problems with free right end point and free end-time and with mixed pointwise constraints. To deal with the problem, we first establish first- and second-order optimality conditions for a reduced problem with fixed end-time. We then obtain optimality conditions for the original problem.

Theoretical Justification and Error Analysis for Slender Body Theory with Free Ends

Slender body theory is a commonly used approximation in computational models of thin fibers in viscous fluids, especially in simulating the motion of cilia or flagella in swimming microorganisms. In [23], we developed a PDE framework for analyzing the error introduced by the slender body approximation for closed-loop fibers with constant radius $\epsilon$, and showed that the difference between our closed-loop PDE solution and the slender body approximation is bounded by an expression proportional to $\epsilon|\log\epsilon|$. Here we extend the slender body PDE framework to the free endpoint setting, which is more physically relevant from a modeling standpoint but more technically demanding than the closed loop analysis. The main new difficulties arising in the free endpoint setting are defining the endpoint geometry, identifying the extent of the 1D slender body force density, and determining how the well-posedness constants depend on the non-constant fiber radius. Given a slender fiber satisfying certain geometric constraints at the filament endpoints and a one-dimensional force density satisfying an endpoint decay condition, we show a bound for the difference between the solution to the slender body PDE and the slender body approximation in the free endpoint setting. The bound is a sum of the same $\epsilon|\log\epsilon|$ term appearing in the closed loop setting and an endpoint term proportional to $\epsilon$, where $\epsilon$ is now the maximum fiber radius.

A direct method for solving calculus of variations problems using the whale optimization algorithm

A numerical algorithm for solving problems of calculus of variations is proposed and analyzed in the present paper. The method is based on direct minimizing the functional in its discrete form with finite dimension. To solve the resulting optimization problem , the recently proposed whale optimization algorithms is used and adopted. The method proposed in this work is capable of solving constrained and unconstrained problems with fixed or free endpoint conditions. Numerical examples are given to check the validity and accuracy of the proposed method in practice. The results show the superior accuracy and efficiency of the proposed technique as compared to other numerical methods.