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Mathematical Methods for Advanced Problems of Inventory Control
No full textWe study infinite horizon stochastic inventory problems with general demand distributions
and piecewise linear concave ordering costs. Such costs arise in the important cases of
quantity discounts or multiple suppliers. We consider the case of concave costs involving two
linear segments. This corresponds to the case of one supplier with a fixed cost, a variable
cost up to a given order quantity, and a quantity discount beyond that, or equivalently,
the case of two suppliers, one with a low fixed cost along with a high variable cost and the
other with a high fixed cost along with a low variable cost. It is well understood that for
a stochastic inventory control problem with a fixed cost and a per-unit variable cost, an
(s, S) policy is optimal when there is only one supplier. In this work we address the case of
multiple suppliers under several different scenarios.
We provide a rigorous mathematical proof of the optimality of several inventory control
models, which will help managers make better business decisions regarding procurement
policies when facing multiple supply sources and/or quantity discounts for big purchases.
Broadly, there are two main areas to explore in the realm of inventory control. The first is
lost sales and the second is backlog sales. Our study examines both of these crucial areas.
Our analysis is concerned with the generalization of the classical (s, S) policy for general
demand distributions under a variety of modifications to the classical work of Scarf [36].
In particular, for the lost sales case, we show that certain three and four parameter generalizations of the classical (s, S) policy are optimal. Our contributions consist of generalizing
the demand, solving a functional Bellman equation for the value function that arises in the
infinite horizon framework, and providing an explicit solution in the special case of exponential demand density. We also give conditions under which our generalizations of the (s, S)
policy reduce to the standard (s, S) policy, even though there are two suppliers involved.
Moreover, we provide an explicit solution for the three number policy when the demand
distribution is exponential.
In the other situation, we are concerned with stochastic inventory control problems with
backlog sales during stockout. As was the case for lost sales, we consider both the scenario
in which an optimal selection can be made among two suppliers, as well as the scenario in
which inventory can be purchased with incremental quantity discounts from a single supplier.
We study the problem for arbitrary demand distributions and in infinite horizon. In this
case, we first spell out conditions that guarantee the optimization of (s, S) policy for the
problem under consideration. If these conditions fail to holds, we also demonstrate that a
generalized three parameter policy is optimal in two distinct situations
Framework for Deep Learning on Healthcare Time Series Data
No full textWith recent advances in artificial intelligence, there is an increased demand in the adaptation
of deep learning for decision support systems in consumer applications. Despite the success,
their widespread acceptance, especially in the critical domain of healthcare, has met with
resistance due to challenges in the efficient development of deployable systems. In healthcare,
it is important that not only are the deployed systems high performing, but also are unbiased
and provide a functional understanding of their outcomes in critical decisions. Furthermore,
owing to the distributed nature of healthcare data and requirement of privacy, there is an
acute shortage of good quality data required to train the data hungry black-box deep learning
models which leads to model drift and lack of generalization on deployment. Predominant
research to handle these challenges individually has been focused primarily on 2D data
modality such as X-rays with nascent interest in the 1D time series data modality. A prime
example of challenging 1D time series physiological signal is Electrocardiogram (ECG), used
to diagnose various health conditions such as arrhythmia. The multi-channel structured
nature of ECG signals with spatial P, Q, R, S, T peak features and the distance between
the peaks of the corresponding beats as temporal features motivate their use in empirical
evaluation of our framework. This kind of structured spatial and temporal information in
time series data makes it more challenging to learn.
This dissertation presents a modular framework to address the predominant challenges en-
abling the development of unbiased, explainable, data efficient and high performing health-
care systems for physiological signal classification. Each module of our framework is focused
on addressing one of five challenges namely model explanations, data availability, data qual-
ity, data and model bias, and performance for the development of deep learning decision
support systems. To the best of our knowledge, this is the first approach in the use of
explanations to not only quantify and benchmark 1D Convolution Neural Network model
capacity and quality but also use the generated performance explanations to assert qual-
ity of data samples maximizing the performance and reducing any derogatory effects. This
allows for efficient model development and functional understanding by developers of the
learned spatial, temporal, frequency, and clinical features. Additionally, to address data
limitations in the iterative development of decision support systems, we present a method
to generate synthetic ECG signals for multiple classes of various lengths and demonstrate
significant improvement in model performance using our synthetic data for augmentation.
Our framework also provides a novel tool to interpret and mitigate the presence of bias in
time series datasets and its amplification on training deep learning models for developers.
While the above modules handle various challenges, the models also need to be high per-
forming in classification outcomes for consumer applications. We achieve state-of-the-art
accuracy on the task of arrhythmia classification leveraging the knowledge from both single
and multi-channel models through meta-learning.
Our framework through its various modules provides a thorough evaluation of model per-
formance capacity to developers and equips them with tools and methods to address the
predominant challenges in the development of deployable healthcare decision support sys-
tems
Neuroimmune and Endocrine Interactions Driving Female-biased Mechanisms in Reproductive Physiology and Pain
No full textSex and gender disparities in healthcare have a profound negative impact on women’s health. Until
recently, most preclinical neuroscience research has relied almost entirely on male animals to the
exclusion of females due to perceived confounds by hormonal cycling. The usage of female
animals in preclinical settings in recent years has opened a realm of possibility in neuroscience
research as many groups have demonstrated sex biases in neuroimmune and endocrine crosstalk.
Several disorders exhibit female-biased prevalence, including many chronic pain disorders and
reproductive system disorders. Additionally, treatments for these disorders are often less effective
in women and come with ill-tolerated side effects. Thus, there is a strong need to study female-
biased mechanisms in these disorders to improve therapeutics and patient outcomes. This work
focuses the role of metabolic stress, both cellular and whole-body, in the regulation of female
fertility. First, we induced whole-body metabolic stress via consumption of a high-fat diet by
young female mice and measured changes in estrous cycling and serum progesterone. We found
that a high-fat diet induces transient shifts in estrous cycling and progesterone levels prior to overt
weight gain. Next, we utilized a transgenic mouse model with conditional removal of LKB1 in
peripheral sensory neurons to model neuronal metabolic stress. Females with LKB1 deletion have
greatly enhanced fertility compared to wild-type mice, with no effect of LKB1 removal in male
mice. Further, LKB1 in sensory neurons promotes ovarian innervation. We then utilized a
preclinical model of chronic muscle pain to validate a battery of pain and functional assessments.
Those measurements were directly compared to pain and functional assessments performed in a
clinical trial with women with FM. Finally, we assessed changes in adaptive immune cell
phenotypes before and after treatment with IL-5, a cytokine previously demonstrated to play a
unique role in chronic muscle pain and women with FM. Overall, this work highlights female
biased mechanisms that modulate neuroendocrine communication and fertility and neuroimmune
crosstalk during chronic muscle pain
Testing Quasi-independence With Survival Tree Approaches
No full textThis dissertation aims to address two common issues in survival analysis. First, we develop
a powerful quasi-independence test for survival and recruitment times. The proposed test
extends existing permutation tests by incorporating cutting-edge survival tree algorithms
to achieve high power in detecting various quasi-dependence scenarios. Second, we explore
tools from frailty models, recurrent event models, and meta-analysis while considering the
longitudinal information collected throughout the last decade to understand the risk of injury
and re-injury. The dissertation is organized as follows.
Chapter 2 develops the tree-based method to test the quasi-independence between left trun-
cation time and survival time. Individuals who experienced the event prior to when the
study began are left-truncated. Quasi-independence of truncation and event times refers
to a factorization of their joint density in the observable region (the event time is no less
than the left truncation time). Unlike the assumption of independence between censoring
time and event time, the assumption of quasi-independence between truncation time and
event time can be tested. Existing tools such as the conditional Kendall’s tau test are pow-
erful in detecting monotonic dependencies. Extensions of existing quasi-independent tests
have been proposed to detect non-monotonic alternatives. Thus, the two minimum p-value
tests (minp1 and minp2 tests) are also proposed to test simple non-monotonic dependencies.
In this paper, we develop a powerful and computationally fast tree-based p-value test for
quasi-independence where the data has complicated non-monontonic dependencies. We also
developed different permutation and bootstrap methods to approximate the null distribution
of the tree-based test.
Chapter 3 assesses the aggregated overall effect of different covariates on injury risk during
the eight competitive seasons for soccer players in German Bundesliga. One of the standard
approaches in modeling the risk in recurrent event data is to model the rate function. We
start by stratifying the injury data by season where we assume that the eight Bundesliga
seasons are mutually independent, and the seasons are not interacting with any of the co-
variates. We then apply the Anderson-Gill (AG) model to find the regression coefficients
of the covariates without accounting for overlapping players thus ignoring between seasons
dependence. To solve this issue, we apply the AG model for each season and aggregate
the results by meta-analysis. However, the common meta-analysis models such as the fixed
effects model, and the random effects model assume that there are no overlapping subjects
between studies. Since our data has overlapping players between seasons, we developed
a novel meta-analysis model which can handle our injury data. This new model suggests
that the presence of a pre-season injury, and additional game-time during a match might
be associated with a lower risk of getting a regular season injury. As the number of previ-
ous injuries increases, there might be a higher risk of getting a regular season injury. We
found that the Goalkeeper position is less likely to get injured compared to the Defender
position. In this chapter, we also take into account that the playing condition of a soccer
player will go from “healthy” to “injured” multiple times (alternating gap times) within a
season. The semiparametric estimation approach under the accelerated failure time (AFT)
model was used to evaluate the covariate effects on the two alternating states. To get the
aggregated overall effect, we applied a fixed effects model. From this analysis, we find that
the presence of pre-season injuries and frequent injuries in the past imply shorter healthy
times. Additionally, increased game-time during a season might be associated with longer
healthy times and shorter injury times
Processing and Characterization of CeRAM: a Non-volatile Non-filamentary Resistive Memory
No full textMemory technologies have been evolving for a long time to provide durable and fast operation
while not being very expensive. SRAM, DRAM, and Flash are traditional memories with
advantages over each other in terms of speed, cost, reliability, and non-volatility. In addition,
several emerging memory technologies are coming forward to solve one or more problems
associated with existing memory technologies. CeRAM is one such memory technology projected
to have several benefits over existing memory technologies.
CeRAM, where ‘Ce’ stands for ‘Correlated Electrons’, is a resistive memory that undergoes
switching through orbital interaction of atoms and bandgap variation in the material. In addition
to being non-volatile, CeRAM is seen to have fast switching, and due to a rather simple fabrication
process, CeRAM is relatively less expensive, as well. This gives CeRAM a potential edge over the
existing memory technologies in terms of speed, cost, and memory retention.
This project explores the operation of CeRAM memory devices and how durable and reliable they
can be. The thesis indulges in the fabrication methodology of the device and investigates the
performance through different tests. Stable two-state operation is demonstrated in these memory
devices in terms of setting and resetting. Moreover, these devices offer promising endurance from
room temperature to high-temperature environments (i.e., up to 200C), thereby expanding the
scope of application of these memory devices.
This project attempts to establish a functioning memory device that can work well in terms of
writing or programming the memory, reading the distinctive memory states, competent endurance,
and high-temperature operation. The results are promising, and more work can enhance the
performance of these devices. It can potentially lead to reliable non-volatile memory technology
that does not compromise speed and cost-effectiveness
Improving Science Literacy Through Science Fiction Literature, Films, and Digital Games
No full textThis dissertation demonstrates the role of science fiction literature, films and digital games in
enhancing scientific literacy at a high school level. While there are many ways of teaching
scientific concepts, this project studies how science content may be taught through an analysis of
specific science fiction novels, films, and video games. These works include: the book and film
versions of Michael Crichton’s The Andromeda Strain (1969) and The State of Fear (2004); The
Andromeda Evolution by Daniel H. Wilson (2019) and Change Agent by Daniel Suarez (2017);
the film, Gattaca, written and directed by Andrew M. Niccol (1997;) Naomi Oreskes’ The
Collapse of The Western Civilization (2014); and Kim Stanley Robinson’s New York 2140
(2017) and The Ministry for the Future (2020). Digital games discussed range from Geniverse
(2016), In Other Waters (2020), Perfect Strain (2017), Microscopya (2022), Plague Inc: Evolved
(2015), The Cure (2021), Mission Biotech (2020) to Maroon (2017).
Through an analysis of these SF materials, scientific concepts and issues from bacteriology,
biotechnology, climate change and CRISPR are identified and evaluated for their potential use in
high school science classroom. Each of the science fiction works provide a
coherent narrative that offers students an engaging way to access and understand science in
complex contexts. Whether in the form of novels, films or digital games, high school teachers
could use these materials as entry points to explain scientific concepts and societal themes in
ways the supplement their existing science curricula and learning goals. Used wisely, science
fiction works can develop students’ abilities in thinking critically and scientifically through
imaginative reading and play which in turn fosters the skill- sets needed to become scientifically
literate citizens
Social Security Reforms in Chile: Effects on Poverty, Labor Supply, and Savings
No full textThis dissertation examines the effects of Chile’s solidarity pensions on retirement behavior,
poverty reduction in old age, and the consequences of early pension withdrawals during the
COVID-19 pandemic. The first study analyzes the impact of expanded solidarity pensions
on retirement decisions and poverty rates using a life cycle model for married males and data
from the Chilean Social Protection Survey (EPS). The findings show that increased mini-
mum pensions discourage labor force participation and lead to earlier retirements, while also
reducing poverty among individuals over 65. The second study focuses on the consequences
of early pension withdrawals during the pandemic. Using a life cycle model and taking ad-
vantage of a supplementary section in the EPS on early withdrawals during the pandemic,
the research assesses the effects of these withdrawals on pension wealth, saving rates, and
replacement rates. The findings indicate that early withdrawals significantly reduce private
pension savings at retirement, resulting in lower replacement rates. However, the inclusion
of solidarity pensions helps mitigate the reduction in replacement rates, particularly bene-
fiting those who made withdrawals in their 40s and individuals with middle incomes. This
dissertation provides valuable insights for policymakers and individuals regarding pension
reforms and retirement decisions
Effects of Flux Type and Molar Ratio in the Synthesis of Cerium Germanides
No full textWith the discovery of a new homologous series An+1BnX3n+1 (A = Ce, B = Co, X = Ge), the low
melting main group elements, indium, tin, and bismuth, were evaluated to determine how different
concentrations will influence the outcome of intermetallics syntheses. Different flux molar ratios
were evaluated, and the systematic synthetic approach led to a fresh perspective on the flux role in
the growth of intermetallic compounds of the series An+1BnX3n+1, including the new series members
Ce3Co2Ge7 and Ce4Co3Ge10. The structure determination by powder and single crystal X-ray
diffraction methods are discussed
The Role of Social Communication in Later Language: an Exploratory Study of Infants Later Diagnosed With Autism and Typically Developing Infants
No full textSocial communication refers to the use of verbal and non-verbal skills in social interactions and
encompasses social attention, communication, and symbolic skills. These skills are thought to
play an important role in the development of receptive and expressive language. The overarching
goal of this dissertation is to evaluate associations between early social communication skills and
later language abilities using longitudinal data. The first study in this dissertation explored early
social communication skills across three groups: infants with a high probability for autism, who
are later diagnosed with autism (HP-ASD), infants with a high probability for autism, who are
not later diagnosed with autism (HP-Neg), and infants with a low probability for autism, who are
not later diagnosed with autism (LP-Neg). Early social communication skills are a harbinger for
later cognitive and language development in infants who develop autism. Hence, investigating
these skills in infancy may help shed light on early risk markers and treatment targets. The
objective of this study was to examine group differences in social communication skills and
explore associations between social communication skills measured at 12-months and language
abilities measured at 24-months. HP-ASD infants demonstrated social communication deficits as
early as 12-months-of-age, well before autism diagnoses are considered stable. Overall, social
communication scores were associated with later receptive and expressive language; however,
this association was not significant in the HP-ASD infants. Although previous research has
reported associations between social communication and later language in autistic toddlers, the
current study explored this association in the youngest sample to date. From a developmental
perspective, it is likely that HP-ASD infants had not acquired social communication skills at 12-
months that are associated to later language. The second study explored longitudinal trajectories
of visual social attention to talking faces in typically developing infants, and the third study
explored associations between visual social attention and later language. Previous studies that
have used eye tracking to explore developmental changes in visual social attention to the eyes
and mouth of talking faces have reported a pattern of increasing attention to the mouth starting at
about 8 months of age and peaking at 2 years. This increase in attention to the mouth has been
found to be associated with later expressive language abilities. However, longitudinal eye
tracking data with frequent sampling across development enabled us to capture drastic shifts in
attention between the eyes and mouth of talking faces and enhance our understanding of the
putative relationship between visual social attention and later language abilities. The second and
third studies of this dissertation focused on expanding on existing research by examining visual
social attention in a longitudinal data set and implementing stringent eye tracking quality
controls. Typically developing infants did not demonstrate significant changes in visual social
attention to the eyes and mouth across development, and gaze patterns were not significantly
associated with later language skills. It is likely that a single developmental pattern of visual
social attention did not emerge because of high individual variability and small sample sizes. In
summary, visual social attention measured using eye tracking was not found to support language
development in typically developing infants. However, social communication skills extracted
from an observational standardized assessment were associated with later receptive and
expressive language. Results also presented compelling evidence for early social communication
deficits in HP-ASD infants. The results of this study will inform treatment targets for presymptomatic autism interventions
Towards a High-Performance and Secure Memory System and Architecture for Emerging Applications
No full textIn the 5G era, diverse types of artificial intelligence (AI) and Internet of Things (IoT)
applications emerge in our life, such as smart homes, virtual reality, and autonomous vehicles.
These applications typically impose diversified requirements in real deployments in terms of
latency, privacy, security, etc., and stimulate the evolution and prosperity of heterogeneous
computing. In this dissertation, heterogeneous computing indicates the scheme in which
the different computing Processing Units (PUs) with differentiated computing capacities are
effectively coordinated and managed to achieve computing gains. The representative PUs
include CPU, Graphics Processing Unit (GPU), Field Programmable Gate Array (FPGA),
Application-Specific Integrated Circuits (ASIC), and etc.
As GPU has become one of the most promising and prevalent platforms to deploy emerging
AI-enabled applications, this dissertation sets to discuss some key challenges and solutions
of GPU-based heterogeneous system/architecture, especially the memory subsystem and
management, matching the deployment requirements of emerging applications from the performance and security perspective.
Regarding the challenges, the applications typically process huge volumes of data and computations and are memory-hungry, and can exhibit diverse computation properties and memory
access patterns. In contrast, the GPU-based heterogeneous system/architecture, especially the GPU device, has limited memory capacity. Also, the CPU PU and GPU PU in the heterogeneous system have fundamentally different computing architectures and differentiated
memory subsystems. Thus, there exists a ”memory wall” caused by the mismatch between
the diversified applications properties and the GPU-based system heterogeneity, which damages the applications’ performance. On the other hand, applications face a variety of security and privacy risks during deployments. However, the GPU-based heterogeneous system,
especially the memory subsystem, can expose multiple security vulnerabilities, damaging
applications’ privacy.
To address the challenges, we propose a memory and computing coordinated methodology
to thoroughly exploit the characteristics and capabilities of the GPU-based heterogeneous
system to effectively optimize applications’ performance and privacy. Specifically, 1) we
propose a task-aware and dynamic memory management mechanism to co-optimize applications’ latency and memory footprint, especially in multitasking scenarios. 2) We propose
a novel latency-aware memory management framework that analyzes the application characteristics and hardware features to reduce applications’ initialization latency and response
time. 3) We develop a new model extraction attack that explores the vulnerability of the
GPU unified memory system to accurately steal private DNN models. 4) We propose a
CPU/GPU Co-Encryption mechanism that can defend against a timing-correlation attack
in an integrated CPU/GPU platform to provide a secure execution environment for the edge
applications.
This dissertation aims at developing a high-performance and secure memory system and
architecture in GPU heterogeneous platforms to deploy emerging AI-enabled applications
efficiently and safely