Optimal design of personalized prostate cancer therapy using Infinitesimal Perturbation Analysis

The standard treatment for advanced prostate cancer is hormone therapy in the form of continuous androgen suppression (CAS), which unfortunately frequently leads to resistance and relapse. An alternative scheme is intermittent androgen suppression (IAS), in which patients are submitted to cycles of treatment (in the form of androgen deprivation) and off-treatment periods in an alternating manner. In spite of extensive recent clinical experience with IAS, the design of ideal protocols for any given patient remains a challenge. The level of prostate specific antigen (PSA) is frequently monitored to determine when patients will be taken off therapy and when therapy will resume. In this work, we propose a threshold-based policy for optimal IAS therapy design that is parameterized by lower and upper PSA threshold values and is associated with a cost metric that combines clinically relevant measures of therapy success. We use a Stochastic Hybrid Automaton (SHA) model of prostate cancer evolution under IAS and perform Infinitesimal Perturbation Analysis (IPA) to adaptively adjust PSA threshold values so as to improve therapy outcomes. We also apply this methodology to clinical data from real patients, and obtain promising results and valuable insights for personalized IAS therapy design.     

Dynamic optimal strategy for monitoring disease recurrence

Surveillance to detect cancer recurrence is an important part of care for cancer survivors.In this paper we discuss the design of optimal strategies for early detection of disease recurrence based on each patient’s distinct biomarker trajectory and periodically updated risk estimated in the setting of a prospective cohort study.We adopt a latent class joint model which considers a longitudinal biomarker process and an event process jointly,to address heterogeneity of patients and disease,to discover distinct biomarker trajectory patterns,to classify patients into different risk groups,and to predict the risk of disease recurrence.The model is used to develop a monitoring strategy that dynamically modifies the monitoring intervals according to patients’ current risk derived from periodically updated biomarker measurements and other indicators of disease spread.The optimal biomarker assessment time is derived using a utility function.We develop an algorithm to apply the proposed strategy to monitoring of new patients after initial treatment.We illustrate the models and the derivation of the optimal strategy using simulated data from monitoring prostate cancer recurrence over a 5-year period.     

Heuristics for integrated optimization of catheter positioning and dwell time distribution in prostate HDR brachytherapy

High dose-rate (HDR) brachytherapy is one kind of radiotherapy used to treat different forms of cancer, such as prostate cancer. When this treatment is used for prostate cancer, a radioactive source is moved through catheters implanted into the prostate. For each patient, a treatment plan is constructed. This plan determines for example catheter positions and dwell time distribution, that is, where to the radioactive source should stop and for how long.     

Strengthening the security of authenticated key exchange against bad randomness

Recent history has revealed that many random number generators (RNGs) used in cryptographic algorithms and protocols were not providing appropriate randomness, either by accident or on purpose. Subsequently, researchers have proposed new algorithms and protocols that are less dependent on the RNG. One exception is that all prominent authenticated key exchange (AKE) protocols are insecure given bad randomness, even when using good long-term keying material. We analyse the security of AKE protocols in the presence of adversaries that can perform attacks based on chosen randomness, i.e., attacks in which the adversary controls the randomness used in protocol sessions. We propose novel stateful protocols, which modify memory shared among a user’s sessions, and show in what sense they are secure against this worst case randomness failure. We develop a stronger security notion for AKE protocols that captures the security that we can achieve under such failures, and prove that our main protocol is correct in this model. Our protocols make substantially weaker assumptions on the RNG than existing protocols.     

Prädikative versus funktionale Denkvorgänge beim Konstruieren von Algorithmen

Seen from a historical point of view, two approaches to the formation of mathematical knowledge can be distinguished: classical Greek substantiated inferential knowledge and ancient oriental functional knowledge. As might have been expected, both approaches are not equally well-suited to develop and handle particular concepts. Bateson’s analysis of the term «switch» exposes only fundamental functional features but no predicative ones. Consequently, there is a special demand for functional cognitive activities when solving problems that involve the use and control of the functioning of switching constituents. Within the framework of the DFG-project “Individual differences in the cognition of mathematical concept formation”, the ability of subjects to construct machines that carry out organisational or computational tasks with the help of given mechanical switches and additional connective building blocks have been tested. The construction procedures show pronounced differences. Furthermore, the case or difficulty to get involved with the planning and realisation of the process are reflected in the verbal protocols of the subjects. Their mental attitude corresponds nicely to their behaviour when working on logical problems as they appear in the QuaDiPF-tasks. For the machines see also: http://www.ikm.uos.de/oktivitaeten/dl/dynamic_labyrinths/dynamic-labyrinths.html     

The determination of optimal treatment plans for Volumetric Modulated Arc Therapy (VMAT)

The success of radiation therapy depends on the ability to deliver the proper amount of radiation to cancerous cells while protecting healthy tissues. As a natural consequence, any new treatment technology improves quality standards concerning primarily this issue. Similar to the widely used Intensity Modulated Radiation Therapy (IMRT), the radiation resource is outside of the patient’s body and the beam is shaped by a multi-leaf collimator mounted on the linear accelerator’s head during the state-of-the-art Volumetric Modulated Arc Therapy (VMAT) as well. However, unlike IMRT, the gantry of the accelerator may rotate along one or more arcs and deliver radiation continuously. This property makes VMAT powerful in obtaining high conformal plans in terms of dose distribution; but the apertures are interdependent and optimal treatment planning problem cannot be decomposed into simpler independent subproblems as a consequence. In this work, we consider optimal treatment planning problem for VMAT. First, we formulate a mixed-integer linear program minimizing total radiation dose intensity subject to clinical requirements embedded within the constraints. Then, we develop efficient solution procedures combining Benders decomposition with certain acceleration strategies. We investigate their performance on a large set of test instances obtained from an anonymous real prostate cancer data.     

Fast stepwise procedures of selection of variables by using AIC and BIC criteria

Fast stepwise procedures of selection of variables by using AIC and BIC criteria are proposed in this paper. We shall use a short name “FSP” for these new procedures. FSP are similar to the well-known stepwise regression procedures in computing steps. But FSP have two advantages. One of these advantages is that FSP are definitely convergent with a faster rate in finite computing steps. Another advantage is that FSP can be used for large number of candidate variables. In this paper we also show some asymptotic properties of FSP, and some simulation results.     

Stopping rules in <Emphasis Type="Italic">k</Emphasis>-adaptive global random search algorithms

In this paper we develop a methodology for defining stopping rules in a general class of global random search algorithms that are based on the use of statistical procedures. To build these stopping rules we reach a compromise between the expected increase in precision of the statistical procedures and the expected waiting time for this increase in precision to occur.     

The solution of unconfined seepage problem using Natural Element Method (NEM) coupled with Genetic Algorithm (GA)

Phreatic line detection is a major challenge in seepage problems which should be solved by iterative solving procedures. In conventional methods such as finite element method (FEM), an updating mesh is needed in each iteration where the qualities of the mesh and the nodal connectivity have significant impact on the results. The main aim of this study is to use a method not to be sensitive to mesh generation.     

MIP Models and BB Strategies in Brachytherapy Treatment Optimization

Brachytherapy (brachy being derived from a Greek word meaning short) is the treatment by means of radioactive sources that are placed at short distances from the target cells. This form of therapy is becoming common in the treatment of early stage prostate cancer, the most common cancer and the second leading cause of cancer deaths among American males. We consider the use of mixed-integer programming (MIP) models and branch-and-bound (BB) methods to optimize the placement within the prostate of the radioactive seeds used in this procedure. Several different optimization models are considered along with a number of branchand- bound strategies. With appropriate combinations of modelling and solution strategies, nearoptimal seed placements can be generated for each two-dimensional ultrasound section of the prostate in less than five minutes on a 333-MHz workstation. The original three-dimensional problem can then be solved by considering an appropriately interrelated sequence of these two-dimensional problems.     

Asymptotically optimal pointwise and minimax quickest change-point detection for dependent data

We consider the quickest change-point detection problem in pointwise and minimax settings for general dependent data models. Two new classes of sequential detection procedures associated with the maximal “local” probability of a false alarm within a period of some fixed length are introduced. For these classes of detection procedures, we consider two popular risks: the expected positive part of the delay to detection and the conditional delay to detection. Under very general conditions for the observations, we show that the popular Shiryaev–Roberts procedure is asymptotically optimal, as the local probability of false alarm goes to zero, with respect to both these risks pointwise (uniformly for every possible point of change) and in the minimax sense (with respect to maximal over point of change expected detection delays). The conditions are formulated in terms of the rate of convergence in the strong law of large numbers for the log-likelihood ratios between the “change” and “no-change” hypotheses, specifically as a uniform complete convergence of the normalized log-likelihood ratio to a positive and finite number. We also develop tools and a set of sufficient conditions for verification of the uniform complete convergence for a large class of Markov processes. These tools are based on concentration inequalities for functions of Markov processes and the Meyn–Tweedie geometric ergodic theory. Finally, we check these sufficient conditions for a number of challenging examples (time series) frequently arising in applications, such as autoregression, autoregressive GARCH, etc.     

Wavelet-Based Detection of Outliers in Time Series

This article considers the problem of detecting outliers in time series data and proposes a general detection method based on wavelets. Unlike other detection procedures found in the literature, our method does not require that a model be specified for the data. Also, use of our method is not restricted to data generated from ARIMA processes. The effectiveness of the proposed method is compared with existing outlier detection procedures. Comparisons based on various models, sample sizes, and parameter values illustrate the effectiveness of the proposed method.     

Mesh selection for discrete solution of boundary problems in ordinary differential equations

Numerische Mathematik - In order to use finite difference approximations with non-uniform meshes in boundary value problems, it is necessary to develop procedures for mesh selection. In this paper...     

Optimal treatments for photodynamic therapy

Medical applications in operations research have flourished over the last few decades, and one of the most prolific topics has been how to optimally design cancer treatments. The preponderance of this research has considered radiotherapy design, but several new procedures are emerging as alternatives to standard treatments. This paper addresses the developing treatment modality called photodynamic therapy (PDT), which uses the light-harvesting properties of a photosensitizer. The premise is that cells expire due to a toxic reaction caused by exposing a photosensitizer to a specific wavelength of light. The purpose of treatment design is to decide how to best treat the patient, meaning that cancerous tissues are damaged but that surrounding organs are not. This paper has two objectives. First, we develop a model that allows us to explore the design process. In particular, we develop a standard pharmacokinetic model to estimate the absorption and elimination of the photosensitizer. The biological model provides the data to cast the design process as a time dependent linear program. Second, we use the linear program to answer the question of whether or not PDT is a viable treatment for deep tissue cancers with the only drug currently approved in the USA. Our results indicate that even under optimal conditions, the treatments based on the currently approved drug are not capable of targeting tumors without destroying surrounding tissues. However, a treatment’s success significantly increases with the drug’s affinity for cancerous tissues. The authors are grateful for the comments of the editor and the referee on the original submission.     

Properties of Prior and Posterior Distributions for Multivariate Categorical Response Data Models

In this article, we model multivariate categorical (binary and ordinal) response data using a very rich class of scale mixture of multivariate normal (SMMVN) link functions to accommodate heavy tailed distributions. We consider both noninformative as well as informative prior distributions for SMMVN-link models. The notation of informative prior elicitation is based on available similar historical studies. The main objectives of this article are (i) to derive theoretical properties of noninformative and informative priors as well as the resulting posteriors and (ii) to develop an efficient Markov chain Monte Carlo algorithm to sample from the resulting posterior distribution. A real data example from prostate cancer studies is used to illustrate the proposed methodologies.     

A Mathematical Model of Intermittent Androgen Suppression for Prostate Cancer

For several decades, androgen suppression has been the principal modality for treatment of advanced prostate cancer. Although the androgen deprivation is initially effective, most patients experience a relapse within several years due to the proliferation of so-called androgen-independent tumor cells. Bruchovsky et al. suggested in animal models that intermittent androgen suppression (IAS) can prolong the time to relapse when compared with continuous androgen suppression (CAS). Therefore, IAS has been expected to enhance clinical efficacy in conjunction with reduction in adverse effects and improvement in quality of life of patients during off-treatment periods. This paper presents a mathematical model that describes the growth of a prostate tumor under IAS therapy based on monitoring of the serum prostate-specific antigen (PSA). By treating the cancer tumor as a mixed assembly of androgen-dependent and androgen-independent cells, we investigate the difference between CAS and IAS with respect to factors affecting an androgen-independent relapse. Numerical and bifurcation analyses show how the tumor growth and the relapse time are influenced by the net growth rate of the androgen-independent cells, a protocol of the IAS therapy, and the mutation rate from androgen-dependent cells to androgen-independent ones.

---

     

Auxiliary tool allocation in flexible manufacturing systems

This paper analyses a new approach to the machine loading problem arising in flexible manufacturing systems (FMSs). This approach allows the operations to be assigned to machines assuming that machines have access to all the tools required for their operations. This exploits the flexibility of the FMS completely. Next an allocation of tools to machines is determined which satisfies the tool requirements for each machine and minimizes the total number of tools. Thus this approach minimizes the unnecessary tool duplications in the system and maximizes the tool utilization. The problem is modeled as an integer linear program (ILP). We notice that the main problem has a block diagonal structure which is decomposable by relaxing a set of linking constraints. Each separated sub-problem represents a problem of allocation of a single type of tools. We develop a branch-and-bound based exact solution procedure and three heuristic procedures to solve the sub-problems. Our lower bounding approach uses Lanrangean relaxation. The solutions to the Lagrangean relaxation are further used to determine the branching sequences and to develop heuristic approaches. Since finding even a feasible solution to the main problem is NP-hard, we develop only enumerative procedures to solve the main problem. Finally, these solution procedures are tested on randomly generated test problems.     

New relationships for multi-neighborhood search for the minimum linear arrangement problem

We develop a series of theorems about the graph structure of the classical Minimum Linear Arrangement (MinLA) problem which disclose properties that can be exploited by Multi-Neighborhood Search (MNS) algorithms. As a foundation, we differentiate between swaps of labels attached to adjacent and non-adjacent nodes to create two new neighborhood classes, and show how our theorems yield efficient algorithms for updating key arrays used by local search procedures. In addition, we introduce a class of neighborhoods called set-based neighborhoods supported by a theorem that identifies solutions (labelings) for the MinLA problem in polynomial time that dominate exponential numbers of alternative solutions. The component neighborhoods within this new neighborhood class can be applied in various sequences in conjunction with the first two new neighborhoods introduced. Our results also apply to problems with objectives different than those of MinLA. Finally, our results make it possible to exploit the new neighborhoods according to the user's choice of MNS protocols and alternative local search algorithms.     

Adaptive server staffing in the presence of time-varying arrivals: a feed-forward control approach

We study the short-term staffing problem of systems that experience random, non-stationary demand. The typical method to accommodate changes in arrival rate is to use historical data to identify peak periods and associated forecasting for upcoming time windows. In this paper, we develop a method that instead detects change as it happens. Motivated by an automatic call distributor system in a call centre with time-varying arrivals, we propose a change detection algorithm based upon non-homogeneous Poisson processes. The proposed method is general and may be thought of as a feed-forward strategy, in which we detect a change in the arrival process, estimate the new magnitude of the arrival rate, and assign an appropriate number of servers to the tasks. The generalized likelihood ratio statistic is used and a recommendation for its decision limit is developed. Simulation results are used to evaluate the performance of the detector in the context of a telephone call centre.     

基于Benford法则的舞弊检测方法研究

根据Benford法则,统计数据的有效数字分布概率符合对数规律,人为的舞弊活动将破坏这种规律,本文将这一原理应用到审计工作中,研究这一种基于数字分布规律检测的舞弊检测方法,并提供了专用分析工具。与采用传统的分析性复核的舞弊检测手段比较,本方法基于详细交易数据,具有客观性、指向性、可操作性较强的优点。