Ami Radunskaya

Pomona College · Department of Mathematics

This paper describes a predictive control method to search for unstable periodic orbits of the generalized tent map. The invariant set containing periodic orbits is a repelling set with a complicated Cantor-like structure. Therefore, a simple local stabilization of the orbit may not be enough to find a periodic orbit, due to the small measure of th...

The logistic map is a nonlinear difference equation well studied in the literature, used to model self-limiting growth in certain populations. It is known that, under certain regularity conditions, the stochastic logistic map, where the parameter is varied according to a specified distribution, has a unique invariant distribution. In these cases we...

The interaction of nanoparticles with Caco-2 monolayers in cell culture underpins our predictions of the uptake of nanoformulations in vivo for drug delivery. Cell-penetrating peptides (CPP), such as oligoarginine, are currently of interest to enhance cellular uptake of bioactives and nanoparticles. This paper assesses the cellular association of p...

Purpose We examine the impacts of dosing strategies of plasmids on bacterial communities in the murine gut by measuring the quantity of plasmids in mouse feces. Methods We fed mice carrier bacteria, E. coli , that contain plasmids with both a reporter gene and an antibiotic resistant gene. We varied the quantity of the plasmid-carrying bacteria an...

We present a blood ethanol concentration compartment model which utilizes an animal’s ethanol intake, food intake, and weight to predict the animal’s blood ethanol concentration at any given time. By incorporating the food digestion process into the model we can predict blood ethanol concentration levels over time for a variety of drinking and eati...

This paper describes a predictive control method to search for unstable periodic orbits of the generalized tent map. The invariant set containing periodic orbits is a repelling set with a complicated Cantor-like structure. Therefore, a simple local stabilization of the orbit may not be enough to find a periodic orbit, due to the small measure of th...

Background Fatal overdoses from opioid use and substance disorders are increasing at an alarming rate. One proposed harm reduction strategy for reducing overdose fatalities is to place overdose prevention sites—commonly known as safe injection facilities—in proximity of locations with the highest rates of overdose. As urban centers in the USA are t...

Background: Fatal overdoses from opioid use and substance disorders are increasing at an alarming rate. One proposed harm reduction strategy for reducing overdose fatalities is to place overdose prevention sites - commonly known as safe injection facilities - in proximity of locations with the highest rates of overdose. As urban centers in the Unit...

The last decade has seen a surge of interest in understanding the functional relationships between the elements that make up the diverse ecology of the gut microbiome. This ecological web includes bacteria, viruses, and microbes that enter, populate and leave living hosts. They affect metabolism and stimulate the immune system, directly or indirect...

Charge coupled device (CCD) based, frequency-domain thermoreflectance imaging can be used to characterize the thermophysical properties of solid-state materials, as well as electronic and optoelectronic devices. A four-bucket algorithm is used to obtain the amplitude and phase of the thermoreflectance signal, i.e. the relative change in reflectance...

Charge coupled device (CCD)-based thermoreflectance imaging using a “4-bucket” lock-in imaging algorithm is a well-established, powerful method for obtaining high spatial and thermal resolution two-dimensional thermal maps of optoelectronic, electronic, and micro-electro-mechanical systems devices. However, the technique is relatively slow, limitin...

Members of social groups risk infection through contact with those in their social network. Evidence that social organization may protect populations from pathogens in certain circumstances prompts the question as to how social organization affects the spread of ectoparasites. The same grooming behaviors that establish social bonds also play a role...

Thousands of people each year succumb to complications from deep vein thrombosis (DVT). DVT occurs when blood flow in the veins is blocked by a clot. Individuals with DVT are at increased risk of experiencing pulmonary embolism (PE), in which small pieces of the clot break off and travel to the lungs. PE can lead to lung damage and even death. Mech...

The Women in Mathematics Symposia are a collection of annual regional mathematics conferences for women mathematicians which have all been organized by EDGE affiliates. To the best of our knowledge, they exist in California, the Midwest, Texas, the Carolinas, and Israel. We explore the history and original motivations of the WiMSoCal organizers and...

We simulate a non-human primate's alcohol drinking pattern in order to better understand temporal patterning of alcoholic drinks that can lead to the excessive intakes associated with alcohol use disorder. A stochastic mathematical model of alcohol consumption pattern is developed, where model parameters are calibrated to an individual monkey's dri...

In many social species, there exist a few highly connected individuals living among a larger majority of poorly connected individuals. Previous studies have shown that, although this social network structure may facilitate some aspects of group-living (e.g., collective decision-making), these highly connected individuals can act as super-spreaders...

Individuals living in social groups are susceptible to disease spread through their social networks. The network’s structure including group stability, clustering, and an individual’s behavior and affiliation choice all have some impact on the effect of disease spread. Moreover, under certain scenarios, a social group may change its own structure t...

This paper begins to build a theoretical framework that would enable the pharmaceutical industry to use network complexity measures as a way to identify drug targets. The variability of a betweenness measure for a network node is examined through different methods of network perturbation. Our results indicate a robustness of betweenness centrality...

Here we present a mathematical model of movement in an abstract space representing states of cellular differentiation. We motivate this work with recent examples that demonstrate a continuum of cellular differentiation using single cell RNA sequencing data to characterize cellular states in a high-dimensional space, which is then mapped into ℝ 2...

Conventional differential expression analyses have been successfully employed to identify genes whose levels change across experimental conditions. One limitation of this approach is the inability to discover central regulators that control gene expression networks. In addition, while methods for identifying central nodes in a network are widely im...

Primers used for real-time quantitative PCR. (DOCX)

The gene regulatory network used as a reference network. (XLSX)

References associated with the supplementary information. (DOCX)

Etv5 expression in 6-week-old optic glioma-bearing mice. Etv5 RNA expression is higher in 6-week-old optic glioma-bearing mice relative to control non-neoplastic optic nerves (three samples for each experimental group; p = 0.0113). Note that there is no overlap in the expression of ETV5 for the control versus optic glioma-bearing nerves. (TIFF)

Comparison of closeness measures in the normal and tumor networks. Filled (red) circles indicate genes whose betweenness measure is at least 1.1 times as large in the tumor network as in the normal network and either a tumor betweenness or normal betweenness value greater than 1e6 (identified in the body of the manuscript). These genes are listed i...

Nf1-independent regulation of Etv5 expression in primary astrocytes. No differences in Etv5 mRNA expression were observed between wild-type and Nf1-deficient astrocytes, as assessed by quantitative real-time RT-PCR. Three independently-generated pairs of wild-type and Nf1-/- primary brainstem astrocytes were generated, and maintained as previously...

To increase the speed of thermoreflectance imaging, we derive detailed statistical models of both the conventional imaging algorithm and our proposed higher speed technique, and we experimentally confirm both the models and resulting speed enhancement.

Here we present a mathematical model of movement in an abstract space representing states of cellular differentiation. We motivate this work with recent examples that demonstrate a continuum of cellular differentiation using single cell RNA sequencing data to characterize cellular states in a high-dimensional space, which is then mapped into ℝ ² or...

Therapeutic vaccines play a large role in the cast of immunotherapies that are now an essential component in most cancer treatment regimes. The complexity of the immune response and the ability of the tumour to mount a counter-offensive to this response have made it difficult to predict who will respond to what treatments, and for clinicians to opt...

Random fluctuations of an environment are common in ecological and economical settings. We consider a family of concave quadratic polynomials on the unit interval that model a self-limiting growth behavior. The maps are parametrized by an independent, identically distributed random parameter. We show the existence of a unique invariant ergodic meas...

The cockroach is one of the world’s most prolific and resilient pests, with over 3,500 species worldwide. It is important to understand the growth and adaptive mechanisms of cockroach colonies in order to safely control these populations. We present a continuous time, age-structured population model of the Blattella germanica cockroach that include...

We use a mathematical model to describe the delivery of a drug to a specific region of the brain. The drug is carried by liposomes that can release their cargo by application of focused ultrasound (US). Thereupon, the drug is absorbed through the endothelial cells that line the brain capillaries and form the physiologically important blood-brain ba...

The formation of a thrombus (commonly referred to as a blood clot) can potentially pose a severe health risk to an individual, particularly when a thrombus is large enough to impede blood flow. If an individual is considered to be at risk for forming a thrombus, he/she may be prophylactically treated with anticoagulant medication such as warfarin....

This volume highlights problems from a range of biological and medical applications that can be interpreted as questions about system behavior or control. Topics include drug resistance in cancer and malaria, biological fluid dynamics, auto-regulation in the kidney, anti-coagulation therapy, evolutionary diversification and photo-transduction. Math...

Mathematical models of tumor–immune interactions provide an analytical framework in which to address specific questions regarding tumor–immune dynamics and tumor treatment options. We present a mathematical model, in the form of a system of ordinary differential equations (ODEs), that governs cancer growth on a cell population level. In addition to...

Cancer therapies that harness the actions of the immune response, such as targeted monoclonal antibody treatments and therapeutic vaccines, are relatively new and promising in the landscape of cancer treatment options. Mathematical modeling and simulation of immune-modifying therapies can help to offset the costs of drug discovery and development,...

The immune response is an important factor in the progression of cancer, and this response has been harnessed in a variety of treatments for a range of cancers. In this chapter we develop mathematical models that describe the immune response to the presence of a tumor. We then use these models to explore a variety of immunotherapy treatments, both...

There are a variety of devices for the delivery of pharmaceutical substances, tablets of course being the most prominent. Pharmaceutical scientists and physicians have formulated goals, such as release of a drug in a controlled fashion over an extended period of time or the targeted delivery of a drug to a specific site in a patient’s body. Since e...

We present a new mathematical model of colorectal cancer growth and its response to monoclonal-antibody (mAb) therapy. Although promising, most mAb drugs are still in trial phases, and the possible variations in the dosing schedules of those currently approved for use have not yet been thoroughly explored. To investigate the effectiveness of curren...

B cell chronic lymphocytic leukemia (B-CLL) is known to have substantial clinical heterogeneity. There is no cure, but treatments allow for disease management. However, the wide range of clinical courses experienced by B-CLL patients makes prognosis and hence treatment a significant chal-lenge. In an attempt to study disease progression across diff...

While all ciliates possess nuclear dimorphism, several ciliates - like those in the classes Phyllopharyngea, Spirotrichea, and Armophorea - have an extreme macronuclear organization. Their extensively fragmented macronuclei contain upwards of 20,000 chromosomes, each with upwards of thousands of copies. These features have evolved independently on...

Dendritic cells are a promising immunotherapy tool for boosting an individual's antigen-specific immune response to cancer. We develop a mathematical model using differential and delay-differential equations to describe the interactions between dendritic cells, effector-immune cells, and tumor cells. We account for the trafficking of immune cells b...

Experimental evidence suggests that a tumor's environment may be critical to designing successful therapeutic protocols: Modeling interactions between a tumor and its environment could improve our understanding of tumor growth and inform approaches to treatment. This paper describes an efficient, flexible, hybrid cellular automaton-based implementa...

Mathematical modeling is a vehicle that allows for explanation and prediction of natural phenomena. In this chapter we present guidelines and best practices for developing and implementing mathematical models, using cancer growth, chemotherapy, and immunotherapy modeling as examples.

Matrix tablets are drug delivery devices designed to release a drug in a controlled manner over an extended period of time. We develop a cellular automaton (CA) model for the dissolution and release of a water-soluble drug and excipient from a matrix tablet of water-insoluble polymer. Cells of the CA are occupied by drug, excipient, water or polyme...

We propose a mathematical model for the release of carboxyfluorescein from liposomes whose membrane permeability is modified by the binding of different bile salts to the leaflets of the lipid bilayer. We find that the permeability of the liposomal bilayer depends on the difference in the concentrations of bile salt in the inner and outer leaflets...

In this chapter we develop a mathematical model of the immune response to a weak antigen, suitable for modeling a cancer vaccine. The parameters are calibrated to a murine model and the model is validated by comparing simulations to experimental results. The model is then used to develop a dosing strategy that optimizes the immune response.

The question, how does an organism maintain balance? provides a unifying theme to introduce undergraduate students to the use of mathematics and modeling techniques in biological research. The availability of inexpensive high speed motion capture cameras makes it possible to collect the precise and reliable data that facilitates the development of...

The success of interdisciplinary research teams depends largely upon skills related to team performance. We evaluated student and team performance for undergraduate biology and mathematics students who participated in summer research projects conducted in off-campus laboratories. The student teams were composed of a student with a mathematics backg...

The activation of a specific immune response takes place in the lymphoid organs such as the spleen. We present here a simplified model of the proliferation of specific immune cells in the form of a single delay equation. We show that the system can undergo switches in stability as the delay is increased, and we interpret these results in the contex...

Significance A consumer’s demand for a network good depends on the demands of other consumers, and therefore choosing this demand optimally poses a cognitive challenge for most consumers. In our model of pricing a network good, consumers display “bounded rationality” (in Herbert Simon’s sense), and the vendor chooses a dynamic price path to maximiz...

In this paper we develop two mathematical models to predict the release kinetics of a water soluble drug from a polymer/excipient matrix tablet. The first of our models consists of a random walk on a weighted graph, where the vertices of the graph represent particles of drug, excipient and polymer, respectively. The graph itself is the contact grap...

The aim of the this volume is to showcase original research conducted by newly formed collaborative teams during the IMA's Women in Applied Mathematics (WhAM!) Research Collaboration Conference on Dynamical Systems with Applications to Biology and Medicine. The overarching goal of the workshop was to help build a strong network of women working on...

A continuous-time dynamic model of a network of wind turbines (induction generators) and capacitors connected to a distant bus is developed and implemented in Matlab code in order to study the stability properties of the system. One particular configuration and parameters of the network were provided by Southern California Edison to represent a loc...

During self-paced human walking, the variability in inter- stride intervals exhibit fractal dynamics characterized by long--range correlations having a power-law decay with exponent α. We used diffusion fluctuation analysis (DFA) to estimate α as a function of the roughness of the walking surface for eight (8) healthy subjects (1200-1400 inter- str...

In this paper, we carry out an examination of four mechanisms that can potentially lead to changing morphologies in a growing tumor: variations in nutrient consumption rates, cellular adhesion, excessive consumption of nutrients by tumor cells and immune cell interactions with the tumor. We present numerical simulations using a hybrid PDE-cellular...

We develop and analyze a mathematical model, in the form of a system of ordinary differential equations (ODEs), governing cancer growth on a cell population level with combination immune, vaccine and chemotherapy treatments. We characterize the ODE system dynamics by locating equilibrium points, determining stability properties, performing a bifurc...

Mathematical models of tumor-immune interactions provide an analytic framework in which to address specific questions about tumor-immune dynamics. We present a new mathematical model that describes tumor-immune interactions, focusing on the role of natural killer (NK) and CD8+ T cells in tumor surveillance, with the goal of understanding the dynami...

Recent experimental studies by Diefenbach et al. [1] have brought to light new information about how the immune system of the mouse responds to the presence of a tumor. In the Diefenbach studies, tumor cells are modified to express higher levels of immune stimulating NKG2D ligands. Experimental results show that sufficiently high levels of ligand e...

We present a competition model of tumor growth that includes the immune system response and a cycle-phase-specific drug. The model considers three populations: Immune system, population of tumor cells during interphase and population of tumor during mitosis. Delay differential equations are used to model the system to take into account the phases o...

We present a phase-space analysis of a mathematical model of tumor growth with an immune response and chemotherapy. We prove that all orbits are bounded and must converge to one of several possible equilibrium points. Therefore, the long-term behavior of an orbit is classified according to the basin of attraction in which it starts. The addition of...

This document is intended to provide some background on the basic functions of the human immune system. Please note that this information is by no means comprehensive, and that many of these terms are de ned only in their broadest and least technical sense. Terms in italics are important to understanding the structure of the immune system, and thos...

We present a competition model of cancer tumor growth which includes both the immune system response and drug therapy. This is a four population model which includes tumor cells, host cells, immune cells and drug interaction. We analyze the stability of the drug-free equilibria with respect to the immune response in order to look for target basins...

An analytic and numerical study of the behavior of the linear nonhomogeneous wave equation of the form ε 2 u tt =Δu+f with high wave speed (ε≪1) is carried out. This study was initially motivated by meteorological observations that indicated the presence of large spatial scale gravity waves in the neighborhood of a number of summer and winter storm...

Ways of producing, controlling, and understanding the perception of complexity−particularly as a reflection of natural evolution−is very important in contemporary music composition and is a continuous thread in the author’s works. A series of generativemodels for composition based on characteristics of complex adaptive systems are surveyed. These f...