System Level Synthesis via Dynamic Programming

System Level Synthesis (SLS) parametrization facilitates controller synthesis for large, complex, and distributed systems by incorporating system level constraints (SLCs) into a convex SLS problem and mapping its solution to stable controller design. Solving the SLS problem at scale efficiently is challenging, and current attempts take advantage of special system or controller structures to speed up the computation in parallel. However, those methods do not generalize as they rely on the specific system/controller properties. We argue that it is possible to solve general SLS problems more efficiently by exploiting the structure of SLS constraints. In particular, we derive dynamic programming (DP) algorithms to solve SLS problems. In addition to the plain SLS without any SLCs, we extend DP to tackle infinite horizon SLS approximation and entrywise linear constraints, which form a superclass of the locality constraints. Comparing to convex program solver and naive analytical derivation, DP solves SLS 4 to 12 times faster and scales with little computation overhead. We also quantize the cost of synthesizing a controller that stabilizes the system in a finite horizon through simulations

Development of orthogonally crosslinked thiol-ene hydrogels for encapsulation of pancreatic beta-cells

Type I diabetes mellitus (T1DM) is an autoimmune disease caused by auto-reactive T-cell-mediated destruction of insulin-producing β-cells. Effective encapsulation strategies can protect the transplanted islets from direct attack by host immune cells while maintaining insulin secretion. To achieve this goal, I have developed a hydrogel conformal coating using a visible light-mediated interfacial thiol-ene photopolymerization. Unlike conventional chain-growth visible light polymerizations, no additional cytotoxic co-initiator or co-monomer was required in thiol-ene gelation scheme for rapid gelation. More importantly, islets coated with thiol-ene gel maintained their viability and function in vitro. In addition to microencapsulate β-cells, the second objective of my dissertation focuses on developing a macroencapsulation technique using thiol-ene hydrogel with bioactivity and anti-inflammatory property. While islet transplantation holds potential in permanently reversing T1DM, this procedure initiates a cascade of inflammatory processes. To address this issue, we have developed thiol-ene hydrogel crosslinked by thiolated β-cyclodextrin (βCD). The conjugation of amphiphilic βCD affords enhanced loading and prolonged release of curcumin, an anti-inflammatory drug candidate but with poor water solubility. In addition, bioactive peptide such laminin-derived peptide flanked with two cysteine residues could be readily incorporated through orthogonal crosslinking, thus mimicking extracellular microenvironment in the pancreatic islets. Finally, in order to provide coated β-cells with an ideal biomechanical microenvironment, it is essential to identify a suitable gel stiffness to support the viability and functions of β-cells. To this end, a thiol-allylether hydrogel with on-demand tunable matrix stiffness was developed. Specifically, host molecule βCD was immobilized in the hydrogel network to provide binding sites for soluble guest molecule poly(ethylene glycol)-adamantane. Gel stiffness was tuned through introducing reversible host-guest interactions. After in situ stiffening of the cell-laden hydrogel, the encapsulated β-cells showed increased in insulin mRNA expression, suggesting the profound impact of matrix stiffness on pancreatic β-cell fate

Efficient many-party controlled teleportation of multi-qubit quantum information via entanglement

We present a way to teleport multi-qubit quantum information from a sender to a distant receiver via the control of many agents in a network. We show that the original state of each qubit can be restored by the receiver as long as all the agents collaborate. However, even if one agent does not cooperate, the receiver can not fully recover the original state of each qubit. The method operates essentially through entangling quantum information during teleportation, in such a way that the required auxiliary qubit resources, local operation, and classical communication are considerably reduced for the present purpose

Rapid optimization of working parameters of microwave-driven multi-level qubits for minimal gate leakage

We propose an effective method to optimize the working parameters (WPs) of microwave-driven quantum logical gates implemented with multi-level physical qubits. We show that by treating transitions between each pair of levels independently, intrinsic gate errors due primarily to population leakage to undesired states can be estimated accurately from spectroscopic properties of the qubits and minimized by choosing appropriate WPs. The validity and efficiency of the approach are demonstrated by applying it to optimize the WPs of two coupled rf SQUID flux qubits for controlled-NOT (CNOT) operation. The result of this independent transition approximation (ITA) is in good agreement with that of dynamic method (DM). Furthermore, the ratio of the speed of ITA to that of DM scales exponentially as 2^n when the number of qubits n increases.Comment: 4pages, 3 figure

The Kinetics of Cystatin C: A Marker for Dialysis Adequacy

When 90% or more of native kidney function is lost, renal replacement therapy must be initiated to sustain life. Renal transplantation is the preferred method, but availability is limited. The ideal dialysis prescription remains elusive. Small molecular weight molecules (such as urea and creatinine) have been used as markers of both kidney (native and transplant) and dialysis toxin clearance (function), but there are pitfalls in using these markers to assess total ‘renal’ dose (kidney plus dialysis). Body weight, gender and other factors also affect the concentrations of these small molecules, but not cystatin C. Furthermore, cystatin C has been shown to be a better marker for estimating kidney function than creatinine, and is associated with cardiovascular morbidity and mortality. Studies have shown that it is removed by dialysis. Therefore, we investigated the use of cystatin C, a naturally occurring endogenous protein, as a marker for estimating dialysis adequacy and renal clearance. This investigation was comprised of four studies to understand the kinetics of cystatin C in patients with advanced kidney disease with or without dialysis. We found that the amount of cystatin C reduction was influenced positively by hemodialysis blood flow rate and treatment time, and negatively by ultrafiltration rate. We further demonstrated that renal hyperfiltration significantly influenced the error of creatinine-based glomerular filtrate rate equation, but not for the cystatin C equation. Therefore, cystatin C appears to be a useful marker for the assessment of kidney function in patients with advanced kidney disease but not yet on dialysis. This was taken further in our third study where we developed an equation, which gave a better estimate of residual renal function than previously published equations in patients on dialysis but who have some remaining kidney function. Finally, we confirmed our hypothesis that cystatin C is cleared during dialysis by both diffusion and convection. It is distributed mainly in the extracellular space but equilibrates slowly between the extravascular and intravascular spaces. Furthermore, we have shown that cystatin C while cleared by dialysis is stable between dialysis treatments rather than being influenced by a single dialysis treatment. It is a marker for both dialysis and renal clearances and, thus, gives a stable index of total renal clearance. The long term goal will be to define the cystatin C threshold level that influences patient morbidity and mortality and to allow better dialysis prescriptions for patients with varying (and changing) residual renal function

Optimal quantum algorithm for polynomial interpolation

We consider the number of quantum queries required to determine the coefficients of a degree-d polynomial over GF(q). A lower bound shown independently by Kane and Kutin and by Meyer and Pommersheim shows that d/2+1/2 quantum queries are needed to solve this problem with bounded error, whereas an algorithm of Boneh and Zhandry shows that d quantum queries are sufficient. We show that the lower bound is achievable: d/2+1/2 quantum queries suffice to determine the polynomial with bounded error. Furthermore, we show that d/2+1 queries suffice to achieve probability approaching 1 for large q. These upper bounds improve results of Boneh and Zhandry on the insecurity of cryptographic protocols against quantum attacks. We also show that our algorithm's success probability as a function of the number of queries is precisely optimal. Furthermore, the algorithm can be implemented with gate complexity poly(log q) with negligible decrease in the success probability. We end with a conjecture about the quantum query complexity of multivariate polynomial interpolation.Comment: 17 pages, minor improvements, added conjecture about multivariate interpolatio

Platelet inventory management in blood supply chain under demand and supply uncertainty

Supply chain management of blood and its products are of paramount importance in medical treatment due to its perishable nature, uncertain demand, and lack of auxiliary substitutes. For example, the Red Blood Cells (RBC's) have a life span of approximately 40 days, whereas platelets have a shelf life of up to five days after extraction from the human body. According to the World Health Organization, approximately 112 million blood units are collected worldwide annually. However, nearly 20 percent of units are discarded in developed nations due to being expired before the final use. A similar trend is noticed in developing countries as well. On the other hand, blood shortage could lead to elective surgeries cancellations. Therefore, managing blood distribution and developing an efficient blood inventory management is considered a critical issue in the supply chain domain. A standard blood supply chain (BSC) achieves the movement of blood products (red blood cells, white blood cells, and platelets) from initial collection to final patients in several echelons. The first step comprises of donation of blood by donors at the donation or mobile centers. The donation sites transport the blood units to blood centers where several tests for infections are carried out. The blood centers then store either the whole blood units or segregate them into their individual products. Finally, they are distributed to the healthcare facilities when required. In this dissertation, an efficient forecasting model is developed to forecast the supply of blood. We leverage five years' worth of historical blood supply data from the Taiwan Blood Services Foundation (TBSF) to conduct our forecasting study. With the generated supply and demand distributioins from historial supply and demand data as inputs, a single objective stochastic model is developed to determine the number of platelet units to order and the time between orders at the hospitals. To reduce platelet shortage and outdating, a collaborative network between the blood centers and hospitals is proposed; the model is extended to determine the optimal ordering policy for a divergent network consisting of multiple blood centers and hospitals. It has been shown that a collaborative system of blood centers and hospitals is better than a decentralized system in which each hospital is supplied with blood only by its corresponding blood center. Furthermore, a mathematical model is proposed based on multi-criteria decision-making (MCDM) techniques, in which different conflicting objective functions are satisfied to generate an efficient and satisfactory solution for a blood supply chain comprising of two hospitals and one blood center. This study also conducted a sensitivity analysis to examine the impacts of the coefficient of demand and supply variation and the settings of cost parameters on the average total cost and the performance measures (units of shortage, outdated units, inventory holding units, and purchased units) for both the blood center and hospitals. The proposed models can also be applied to determine ordering policies for other supply chain of perishable products, such as perishable food or drug supply chains.Includes bibliographical references

Photo-click hydrogels prepared from functionalized cyclodextrin and poly(ethylene glycol) for drug delivery and in situ cell encapsulation

Polymers or hydrogels containing modified cyclodextrin (CD) are highly useful in drug delivery applications, as CD is a cytocompatible amphiphilic molecule that can complex with a variety of hydrophobic drugs. Here, we designed modular photoclick thiol-ene hydrogels from derivatives of βCD and poly(ethylene glycol) (PEG), including βCD-allylether (βCD-AE), βCD-thiol (βCD-SH), PEG-thiol (PEGSH), and PEG-norbornene (PEGNB). Two types of CD-PEG hybrid hydrogels were prepared using radical-mediated thiol-ene photoclick reactions. Specifically, thiol-allylether hydrogels were formed by reacting multiarm PEGSH and βCD-AE, and thiol-norbornene hydrogels were formed by cross-linking βCD-SH and multiarm PEGNB. We characterized the properties of these two types of thiol-ene hydrogels, including gelation kinetics, gel fractions, hydrolytic stability, and cytocompatibility. Compared with thiol-allylether hydrogels, thiol-norbornene photoclick reaction formed hydrogels with faster gelation kinetics at equivalent macromer contents. Using curcumin, an anti-inflammatory and anticancer hydrophobic molecule, we demonstrated that CD-cross-linked PEG-based hydrogels, when compared with pure PEG-based hydrogels, afforded higher drug loading efficiency and prolonged delivery in vitro. Cytocompatibility of these CD-cross-linked hydrogels were evaluated by in situ encapsulation of radical sensitive pancreatic MIN6 β-cells. All formulations and cross-linking conditions tested were cytocompatible for cell encapsulation. Furthermore, hydrogels cross-linked by βCD-SH showed enhanced cell proliferation and insulin secretion as compared to gels cross-linked by either dithiothreitol (DTT) or βCD-AE, suggesting the profound impact of both macromer compositions and gelation chemistry on cell fate in chemically cross-linked hydrogels