Neural Operator Variational Inference based on Regularized Stein Discrepancy for Deep Gaussian Processes

Deep Gaussian Process (DGP) models offer a powerful nonparametric approach for Bayesian inference, but exact inference is typically intractable, motivating the use of various approximations. However, existing approaches, such as mean-field Gaussian assumptions, limit the expressiveness and efficacy of DGP models, while stochastic approximation can be computationally expensive. To tackle these challenges, we introduce Neural Operator Variational Inference (NOVI) for Deep Gaussian Processes. NOVI uses a neural generator to obtain a sampler and minimizes the Regularized Stein Discrepancy in L2 space between the generated distribution and true posterior. We solve the minimax problem using Monte Carlo estimation and subsampling stochastic optimization techniques. We demonstrate that the bias introduced by our method can be controlled by multiplying the Fisher divergence with a constant, which leads to robust error control and ensures the stability and precision of the algorithm. Our experiments on datasets ranging from hundreds to tens of thousands demonstrate the effectiveness and the faster convergence rate of the proposed method. We achieve a classification accuracy of 93.56 on the CIFAR10 dataset, outperforming SOTA Gaussian process methods. Furthermore, our method guarantees theoretically controlled prediction error for DGP models and demonstrates remarkable performance on various datasets. We are optimistic that NOVI has the potential to enhance the performance of deep Bayesian nonparametric models and could have significant implications for various practical application

Double Normalizing Flows: Flexible Bayesian Gaussian Process ODEs Learning

Recently, Gaussian processes have been utilized to model the vector field of continuous dynamical systems. Bayesian inference for such models \cite{hegde2022variational} has been extensively studied and has been applied in tasks such as time series prediction, providing uncertain estimates. However, previous Gaussian Process Ordinary Differential Equation (ODE) models may underperform on datasets with non-Gaussian process priors, as their constrained priors and mean-field posteriors may lack flexibility. To address this limitation, we incorporate normalizing flows to reparameterize the vector field of ODEs, resulting in a more flexible and expressive prior distribution. Additionally, due to the analytically tractable probability density functions of normalizing flows, we apply them to the posterior inference of GP ODEs, generating a non-Gaussian posterior. Through these dual applications of normalizing flows, our model improves accuracy and uncertainty estimates for Bayesian Gaussian Process ODEs. The effectiveness of our approach is demonstrated on simulated dynamical systems and real-world human motion data, including tasks such as time series prediction and missing data recovery. Experimental results indicate that our proposed method effectively captures model uncertainty while improving accuracy

Molecular alterations of Ras-Raf-mitogen-activated protein kinase and phosphatidylinositol 3-kinase-Akt signaling pathways in colorectal cancers from a tertiary hospital at Kuala Lumpur, Malaysia

Molecular alterations in KRAS, BRAF, PIK3CA, and PTEN have been implicated in designing targeted therapy for colorectal cancer (CRC). The present study aimed to determine the status of these molecular alterations in Malaysian CRCs as such data are not available in the literature. We investigated the mutations of KRAS, BRAF, and PTEN, the gene amplification of PIK3CA, and the protein expression of PTEN and phosphatidylinositol 3-kinase (PI3K) catalytic subunit (p110α) by direct DNA sequencing, quantitative real-time PCR, and immunohistochemistry, respectively, in 49 CRC samples. The frequency of KRAS (codons 12, 13, and 61), BRAF (V600E), and PTEN mutations, and PIK3CA amplification was 25.0% (11/44), 2.3% (1/43), 0.0% (0/43), and 76.7% (33/43), respectively. Immunohistochemical staining demonstrated loss of PTEN protein in 54.5% (24/44) of CRCs and no significant difference in PI3K p110α expression between CRCs and the adjacent normal colonic mucosa (p = 0.380). PIK3CA amplification was not associated with PI3K p110α expression level, but associated with male cases (100% of male cases vs 56% of female cases harbored amplified PIK3CA, p = 0.002). PI3K p110α expression was significantly higher (p = 0.041) in poorly/moderately differentiated carcinoma compared with well-differentiated carcinoma. KRAS mutation, PIK3CA amplification, PTEN loss, and PI3K p110α expression did not correlate with Akt phosphorylation or Ki-67 expression. KRAS mutation, PIK3CA amplification, and PTEN loss were not mutually exclusive. This is the first report on CRC in Malaysia showing comparable frequency of KRAS mutation and PTEN loss, lower BRAF mutation rate, higher PIK3CA amplification frequency, and rare PTEN mutation, as compared with published reports

A Multipath Mitigation Tracking Architecture Using Adaptive Path Estimator for GPS System

全球定位系統(GPS)可全天候提供精確的位置、速度與時間的資訊給全球的使用者。在GPS系統中，其導航數據資料是利用直接展頻 (DS-SS) 分碼多工的方式進行傳遞。數種誤差來源影響了GPS量測的精確度，包括衛星時脈偏移，電離層延遲，對流層延遲，接收機動態追蹤誤差，多路徑效應與熱雜訊誤差等。理論上而言，經過差分法的技術可以消除所有兩個接收機的共有項誤差。然而多路徑效應因為接收機位置的不同而是無法加以消除，其成為高精度接收機中的主要誤差來源。 一般而言，在GPS參考站與遠端接收機上所發生的多路徑效應是不一樣的。儼然已成為差分式GPS中最顯著的定位誤差來源。在本研究中，我們提出一個動態GPS應用中具有多路徑抑制的接收機系統架構。它包括四個部分: (1)可適性路徑估測器(Adaptive Path Estimator; APE)，(2)多路徑干擾重建器(Multipath Interference Reproducer; MPIR)，(3) 耙式碼延遲鎖相迴路(Rake-based Delay Locked Loop; RB-DLL)，(4) 耙式載波相位鎖相迴路(Rake-based Phase Locked Loop; RB-PLL)。在此僅考慮短路徑延遲所造成之效應(延遲時間在1.5 chip內)。為了在相關領域(Correlation Domain)估測反射路徑參數，我們採用快速傅利葉進行循環相關運算(Circular Correlation)來減少計算複雜度。同時利用可適性路徑估測器來估測多路徑效應中延遲路徑的各項參數。根據前項的預估參數，相對的多路徑成分啟動來完成延遲信號重建的功能。再將複製的延遲信號與具有多路徑效應的信號分別在載波鑑別器與碼鑑別器內部作相減的運算，如此一來便可將已消除多路徑干擾的信號送入耙式碼延遲鎖定迴路與耙式載波相位鎖定迴路中來完成信號同步的功能。 本論文中，我們先對GPS展頻信號及多路徑效應信號特性進行了解，進一步設計可適性多路徑預估器，來估測短延遲時間參數，並將其放入耙式延遲相位鎖定迴路將多路徑干擾予以消除。我們採用Matlab模擬工具來驗證多路徑抑制系統的成效。在GPS室外操作時，在使用一般右手圓極化和半球形態的天線下，可假設所接收到的最小訊號功率約為-154.6 dBW。在一般狀況下，GPS接收機的有效雜訊溫度約為513K，相對應在2-MHz的中頻(IF)頻寬下所生成的熱雜訊功率約為-138.5 dBW。在此假設下針對不同的訊雜比(SNR)，即不同的IF頻寬下，利用可適性耙式延遲相位鎖定迴路，估測(1)反射延遲路徑時間(Reflection Delay Time)，(2)穩態追蹤誤差(Steady-state Tracking Error)，驗證其抑制干擾的成效與表現。The global positioning system (GPS) provides accurate positioning and timing information useful in many applications. The GPS satellites broadcast ranging codes and navigation data with the technique of direct sequence spread spectrum (DS-SS). A wide variety of error sources affect the GPS measurement of pseudorange (also known as code-phase) and integrated Doppler (also known as carrier-phase). Among these are satellite user range error, ionospheric delay, tropospheric delay, receiver dynamic tracking error, multipah and thermal noise. The use of differential techniques theoretically eliminates all error sources which are common to both receivers. The error which remains is multipath, and it becomes the dominant error source in high precision GPS applications. Multipath errors are not identical to the GPS reference station and remote receivers. Thus, it becomes the significant error source in differential GPS. In this research, a multipath mitigation tracking system is presented for dynamic GPS applications. It is comprised of four function blocks, those being (1) adaptive path estimator (APE), (2) multipath interference reproducer (MPIR), (3) Rake-based delay locked loop (RB-DLL), and (4) Rake-based phase locked loop (RB-PLL). Only the short delay condition with delay less than 1.5 PN chip is considered here, because GPS pseudorange error envelope decreases to zero for delay time greater than 1.5 PN chip. In order to estimate reflection profile in the correlation domain, the FFT-based circular correlation and block average method (BAM) are utilized to offer significant savings in computational complexity. The APE estimates the delayed profiles and coefficients of the reflection signals. With the path parameters from APE, the corresponding multipath arms are activated to accomplish the multipath reproduction. These replica profiles are used for subtracting the reflection components from carrier and code discriminators before sending it into the Rake-based carrier/code tracking loops. In this thesis, we first introduce the characteristic of GPS spread-spectrum signal and multipath effect. Then, we design the APE and estimate the short-delay path parameters to perform multipath interference cancellation in the RB-DLL. The simulation results of the multipath mitigation system are obtained by using Matlab tool to verify the performances. In outdoor condition, the received signal power is assumed to be -154.6 dBW, because the minimum received signal power is about this value by using a typical GPS antenna with right-hand circular polarization and a hemispherical pattern. The noise power is assumed to be -138.5 dBW in a 2-MHz IF bandwidth, because a typical effective noise temperature for a GPS receiver is 513K. The reflection delay estimation and steady-state tracking error are conducted at different IF band SNR environments (i.e., different IF bandwidth) via extensive simulation to demonstrate the performances of our proposed adaptive rake-based multipath technique.中文摘要 IX 英文摘要 XI 目錄 XV 圖目錄 XIX 表目錄 XXVII 第一章 緒論 1 1.1 研究背景 1 1.2 研究方向 3 1.3 論文架構 4 第二章 全球定位系統(GPS) 7 2.1 GPS訊號的數學表示模型 7 2.2 GPS訊號之成份與性質 10 2.2.1 GPS導航信息 10 2.2.2 C/A-code展頻碼之特性 14 2.3 GPS訊號與熱雜訊之功率等級(Power Levels) 18 2.4 GPS訊號之捕獲(Acquisition)與追蹤(Tracking) 20 2.4.1 搜尋訊號載波頻率與C/A-code碼相位 21 2.4.2 展頻碼追蹤迴路(Code Tracking Loop) 23 2.4.3 載波相位追蹤迴路(Carrier Phase Tracking Loop) 26 2.4.4 位元同步(Bit Synchronization) 30 2.4.5 資訊位元解調(Data Bit Demodulation) 30 2.5 使用C/A-code量測衛星與接收機間距離(Pseudorange) 30 第三章 多重路徑效應之影響 34 3.1 多重路徑造成之假想距離誤差(Pseudorange Error) 35 3.2 多重路徑造成之載波相位鎖定誤差 40 3.3 多重路徑抑制方法 42 3.3.1 空間性處理(Spatial Processing)技術 43 3.3.2 時間領域處理(Time Domain Processing)技術 45 3.3.3 時間領域處理方法之效能 49 第四章 應用於GPS系統之可適性多路徑追蹤及抑制迴路 51 4.1 多重路徑系統描述 51 4.1.1 所接收之訊號模型 51 4.1.2 提出之鎖相系統描述 53 4.2 可適性路徑估測器(APE) 55 4.2.1 快速傅利葉轉換為基礎之迴旋相關運算 55 4.2.2 可適性路徑估測演算法 58 4.3 多重路徑消除(Multipath Cancellation; MPC)鎖相迴 路 64 4.3.1 耙式碼延遲鎖相迴路(Rake-based Delay Locked Loop) 65 4.3.2 耙式載波相位鎖相迴路(Rake-based Phase Locked Loop) 69 第五章 GPS系統之都卜勒效應(Doppler Effect) 73 5.1 衛星與行動接收機移動所造成之都卜勒頻率偏移 74 5.2 決定汽車行動通訊應用之追蹤迴路相關器積分時間 80 5.3 載波比率輔助(Carrier Rate Aiding)之C/A-code碼延 遲鎖相迴路(DLL)架構 83 第六章 應用於GPS系統之可適性多路徑追蹤及抑制迴路之模擬 與效能比較 86 6.1 中頻(IF)頻帶GPS訊號之產生 88 6.2 將IF訊號降頻並濾波以產生基頻帶I/Q通道訊號 100 6.3 可適性路徑估測器(APE)之I/Q通道訊號強度係數與取樣 展頻碼鎖相誤差估測 116 6.4 可適性路徑估測器之RLS演算法遺忘因子(Forgetting Factor)對路徑估測的影響 128 6.5 IF 頻寬為8.184 MHz、4.092 MHz及2.046 MHz下，標準 相關器、短相關器與閃光相關器型式之DLL鑑別器 137 6.6 模擬中所使用的碼追蹤迴路與載波相位追蹤迴路之迴路 參數設定 142 6.7 無都卜勒效應狀態下(衛星仰角為90°且接收機為靜止狀 態)，所提出之多路徑抑制鎖相系統之模擬及效能並與 標準相關器、短相關器、閃光相關器迴路比較 145 6.8 只考慮衛星所造成之最大都卜勒效應狀態下(衛星仰角 為0°且接收機為靜止狀態)，所提出之多路徑抑制鎖相 系統模擬及效能 172 6.9 考慮衛星所造成之最大都卜勒效應加上裝載GPS接收機 之汽車移動所造成之都卜勒效應下(衛星仰角為0°且接 收機為移動狀態)，所提出之多路徑抑制鎖相系統模擬 及效能 179 第七章 結論與未來展望 186 7.1 結論 186 7.2 未來展望 187 附錄A：證明在無多重路徑干擾下交互相關函數為決定傳輸延遲 之最佳估測器 188 附錄B：領先相關器與落後相關器輸出之雜訊成份相關性推導 191 附錄C：所提出之可適性多路徑追蹤及抑制迴路對於單次要路徑 干擾效能 192 參考文獻 19

The Stability Theory and Design of Two-Dimensional Recursive Digital Filters and Recursive Digital Lattice Filters

二維(2-D)數位全通濾波器(DAF)擁有只在相位上變化的性質，並且已用於補償相位失真的訊號。它的結構有許多令人期望的優點，例如:低硬體複雜度與低的係數量化誤差。它也可以被用於設計多範圍的濾波功能。在本論文中，我們提出二維因果且實係數或負數係數皆被限制於第一象限(QP)之數位全通濾波器的單調遞減相位響應性質。在實係數的情形下，我們也證明出之前文獻所提出的有限輸入有限輸出(BIBO)之相位穩定性條件只是對於QP數位全通濾波器的充分條件，而此穩定性條件對於二維可分離(separable)數位全通濾波器是充分且必要條件。相對於之前文獻所提出的相位穩定性條件，我們提出的相位響應穩定性性質擁有增加相位設計自由度的優點。我們提出的相位響應穩定性性質有一個重要的應用，即是可用來選擇適當且期望的相位規格來設計出穩定的QP數位全通濾波器。 二維非對稱半平面(NSHP)數位全通濾波器擁有較一般化的因果特性，且效能比二維QP數位全通濾波器來的要好。因此，我們也提出二維因果且實係數或負數係數皆被限制於NSHP支撐區域之數位全通濾波器的相位響應性質來決定BIBO穩定性。再者，我們也考慮二維NSHP數位全通濾波器之分子多項式對於穩定性的影響。我們提出的相位響應穩定性性質有許多應用。其中一個重要的應用，即是可用來選擇適當且期望的相位規格來設計出穩定的NSHP數位全通濾波器。我們也提出一個特徵濾波器(eignfilter)設計方法來設計二維NSHP數位全通濾波器來套用上述的應用。 一維(1-D)晶格(lattice)結構數位濾波器擁有低通帶敏感度與對量化誤差的抗性。它的模組化性質更造就了工業上的應用。另外，一維晶格結構數位濾波器對於一維直接形式(direct form)數位濾波器來說有較低的執行複雜度。一維直接形式數位全通濾波器的係數與一維晶格結構數位全通濾波器的反射係數有著一對一映射的性質，然而二維晶格結構數位全通濾波器並無法擁有這個特性。因此，我們提出一個二維晶格架構來實現有一般化因果特性的二維數位全通濾波器。我們採用四種基本晶格區塊來實現擁有類似NSHP係數支撐區域的楔形係數支撐區域之二維數位全通濾波器。我們也提出此二維晶格數位全通濾波器的兩種變異形式之二維晶格結構。我們利用Rosser狀態空間模型來驗證我們所提出的二維晶格數位全通濾波器之最小實現性質。我們提出一個最小平方設計方法(least-squares design)與一個最小最大誤差設計方法(minimax design)來求解所提出二維晶格數位全通濾波器架構產生的非線性最佳化問題。我們所提出二維晶格數位全通濾波器架構的新穎性在於不但繼承了一維Gray-Markel晶格數位全通濾波器架構的優點並且擁有比現存所有二維晶格數位全通濾波器架構的效能要好的優點。接著，我們提出一個並排連結(parallel-combination)結構並使用我們所提出的二維晶格數位全通濾波器架構來設計一般的二維遞迴式濾波器。此提出的二維遞迴式濾波器的新穎性在於不但繼承了所提出二維晶格數位全通濾波器的優秀特性並且擁有比現存使用直接形式NSHP數位全通濾波器來建構的二維遞迴式濾波器的效能要好的優點。A two-dimensional (2-D) digital allpass filter (DAF) has a property of varying only phase with constant magnitude and it has mainly been used as a phase compensator for distorted signals. It is a structure that has some desirable attributes such as low complexity and low coefficient quantization error. It also can be used to design a wide range of filtering functions. In this doctoral dissertation, we present the monotone phase-response property of a two-dimensional (2-D) causal digital allpass filter (DAF) with real coefficients or complex coefficients in the quarter-plane (QP) support region. Regarding the circumstance of real coefficients, we also prove that the previously proposed bounded-input bounded-output (BIBO) stability criterion on the viewpoint of unwrapped phase is necessary and sufficient for 2-D separable DAFs, but is only sufficient for QP DAFs. The resultant property possesses the advantage of increasing the freedom of phase design over the previously proposed one. A remarkable application of the presented property is choosing an appropriate specification for the desired phase response of a 2-D QP DAF design. A 2-D nonsymmetric half-plane (NSHP) recursive DAF possesses more general causality and performs better than a 2-D quarter-plane (QP) recursive DAF. Hence, we also present the phase-response property for the BIBO stability of a 2-D causal recursive DAF with NSHP support region. Both cases of filters with real coefficients and complex coefficients are explored. Moreover, the effect of the numerator polynomial of a 2-D NSHP DAF on stability is also considered. The presented phase-response property has several applications. A remarkable application is that it can be utilized to enforce stability for a 2-D NSHP DAF design by choosing an appropriate phase specification. The eigenfilter design of 2-D NSHP DAFs for this application is also presented. The 1-D lattice filter structure exhibits the attractive advantages of low passband sensitivity and robustness to quantization error. The modularity of this structure makes industrial application. Additionally, 1-D digital lattice filter structure requires lower computational cost than 1-D direct form digital filter. The filter coefficients of 1-D direct-form allpass filter and the reflection coefficients of 1-D lattice allpass filter have a one-to-one mapping relationship. However, 2-D lattice allpass structures always do not have this relationship. Hence, we present a lattice structure for the realization of 2-D recursive DAFs with general causality. We employ four basic lattice sections to realize 2-D recursive DAFs with wedge-shaped coefficient support region like a NSHP support region. Two variations of the 2-D lattice structure are also presented. We use the Roesser state space model to verify the minimal realization of the proposed 2-D recursive lattice DAF. We present a least-squares design technique and a minimax design technique to solve the nonlinear optimization problems of the proposed 2-D lattice DAF structure. The novelty of the presented lattice structure is that it not only inherits the desirable attributes of 1-D Gray-Markel lattice allpass structure but also possesses the advantage of better performance over the existing 2-D lattice allpass structures. Then, we present a parallel-combination structure composed of the 2-D lattice DAFs for the design of 2-D recursive filters. The novelty of the 2-D recursive filter is that it not only inherits the desirable attributes of lattice filters but also possesses the advantage of better performance over the 2-D recursive NSHP filters

Biomechanical evaluation of peripheral nerves after crush injuries

Background: Crush injury of nerves is a common condition but the biomechanical integrity of the human peripheral nerve after crushing is unknown. This study aims to investigate the impact of crush injury on human digital nerves based on different compressive forces. Materials and methods: Twenty digital nerves were harvested from three fresh-frozen cadaver hands. The original diameters of proximal, middle and distal end of nerve segment were measured. The midst of each digital nerve was compressed by a customized mechanical system, at 1N, 3N and 5N for 30sec. The diameters were measured again within 1 minute after the nerve crush test was performed. The digital nerve was then subjected to biomechanical test to measure its ultimate tensile strength, stiffness, maximum stress and strain. Deformity of digital nerve was computed based on the diameter of middle nerve segment before and after crush test. Results: No significant difference was found in between groups for ultimate tensile strength (p=0.598), stiffness (p=0.593), maximum stress (p=0.7) and strain (p=0.666). The deformity of nerves under the compression of 1N, 3N and 5N was computed at 72.1%, 54.2% and 45.9%. The effect of compression on the deformity of nerves was statistically significant (p<0.001). Conclusions: It was found that the compressive forces have no impact on the biomechanical integrity of peripheral nerves but the deformity of nerves could be severely caused by low compressive force. It is suggested that the management of nerve crush injury shall be taken immediately and focus on neurophysiological function and degeneration of nerves for a crush with low compressive force and short duration

Zebrafish larvae exposed to ginkgotoxin exhibit seizure-like behavior that is relieved by pyridoxal-5′-phosphate, GABA and anti-epileptic drugs

SUMMARY The etiology of epilepsy is a very complicated, multifactorial process that is not completely understood. Therefore, the availability of epilepsy animal models induced by different mechanisms is crucial in advancing our knowledge and developing new therapeutic regimens for this disorder. Considering the advantages of zebrafish, we have developed a seizure model in zebrafish larvae using ginkgotoxin, a neurotoxin naturally occurring in Ginkgo biloba and hypothesized to inhibit the formation of the neurotransmitter γ-aminobutyric acid (GABA). We found that a 2-hour exposure to ginkgotoxin induced a seizure-like behavior in zebrafish larvae. This seizure-like swimming pattern was alleviated by the addition of either pyridoxal-5′-phosphate (PLP) or GABA and responded quickly to the anti-convulsing activity of gabapentin and phenytoin, two commonly prescribed anti-epileptic drugs (AEDs). Unexpectedly, the ginkgotoxin-induced PLP depletion in our experimental setting did not affect the homeostasis of folate-mediated one-carbon metabolism, another metabolic pathway playing a crucial role in neural function that also relies on the availability of PLP. This ginkgotoxin-induced seizure behavior was also relieved by primidone, which had been tested on a pentylenetetrazole-induced zebrafish seizure model but failed to rescue the seizure phenotype, highlighting the potential use and complementarity of this ginkgotoxin-induced seizure model for AED development. Structural and morphological characterization showed that a 2-hour ginkgotoxin exposure did not cause appreciable changes in larval morphology and tissues development. In conclusion, our data suggests that this ginkgotoxin-induced seizure in zebrafish larvae could serve as an in vivo model for epileptic seizure research and potential AED screening

Design and Investigation of Core/Shell GQDs/hMSN Nanoparticles as an Enhanced Drug Delivery Platform in Triple-Negative Breast Cancer

Due to the excellent photoluminescent properties and singlet oxygen (¹O₂) generating efficiency, graphene quantum dots (GQDs) with maximal emission in near-infrared region (NIR) exhibited great potential in cancer imaging and therapy. However, GQDs can be cleared quickly via the renal system in vivo because of their ultrasmall size, which leads to the compromised cancer cell killing efficacy. Here, we report a hybrid nanoplatform, where GQDs were incorporated into the cavity of hollow mesoporous silica nanoparticles (hMSN) to form GQDs@hMSN-PEG nanoparticles (NPs). Optical characterization indicated that GQDs@hMSN-PEG NPs still maintained good absorption and emission properties from GQDs, and the composite NPs still possessed similar ¹O₂ generating efficiency. GQDs@hMSN-PEG NPs exhibited good biocompatibility in vitro and in vivo. High cargo-loading efficiency was achieved for doxorubicin (DOX), and the formed GQDs@hMSN­(DOX)-PEG NPs showed the feasibility of tumor-oriented drug delivery. The extended retention time in tumor and good drug loading efficacy confirmed that GQDs@hMSN-PEG could serve as one promising candidate for combinational cancer treatment where photodynamic therapy and chemotherapy modules can be integrated into one system