Optimal Rates of Convergence for Noisy Sparse Phase Retrieval via Thresholded Wirtinger Flow

This paper considers the noisy sparse phase retrieval problem: recovering a sparse signal $x \in \mathbb{R}^p$ from noisy quadratic measurements $y_j = (a_j' x )^2 + \epsilon_j$, $j=1, \ldots, m$, with independent sub-exponential noise $\epsilon_j$. The goals are to understand the effect of the sparsity of $x$ on the estimation precision and to construct a computationally feasible estimator to achieve the optimal rates. Inspired by the Wirtinger Flow [12] proposed for noiseless and non-sparse phase retrieval, a novel thresholded gradient descent algorithm is proposed and it is shown to adaptively achieve the minimax optimal rates of convergence over a wide range of sparsity levels when the $a_j$'s are independent standard Gaussian random vectors, provided that the sample size is sufficiently large compared to the sparsity of $x$.Comment: 28 pages, 4 figure

Stimuli-Responsive Prodrug Nanomaterials for Combination Therapy of Cancer

Cancer is a challenging disease to cure. Current treatment methods mainly include chemotherapy and phototherapy. Chemotherapy drugs, due to their high toxicity and systemic distribution, still cause great suffering for cancer patients. Moreover, the clinical efficacy of single-drug treatment is limited due to the complex pathogenesis of malignant tumors and multi-drug resistance often exhibited by tumor cells. To address these challenges, combination therapy with multiple drugs or multiple treatment modalities is widely used to treat various malignancies. In parallel, the rapid development of nanotechnology has promoted the application of nanomedicines in combination chemotherapy. Still, although nanodrugs can increase the drug concentration in the tumor area, the residual nanodrugs in the liver and kidneys still pose a huge threat to human health. Prodrugs are pharmacologically inactive drugs or compounds that are metabolized into pharmacologically active drugs after ingestion by the human body. Prodrug treatment strategies have become an exploratory direction to address the side effects of chemical therapy. Nanomedicine-based prodrugs can be prepared to improve targeting efficiency by using cancer cell targeting ligands and respond to the slightly acidic and reducing microenvironment of the tumor by using different chemical bonds, which can improve the antitumor effect and reduce the toxic side effects on healthy tissues. In this thesis, we designed prodrug-based nanomaterials and studied the antitumor effects of the prodrugs using different drug delivery systems. First, reduction-sensitive paclitaxel (PTX) prodrugs were synthesized as connecting units to achieve synergistic treatment of cancer chemotherapy and photodynamic therapy using reactive oxygen species to treat cancer cells. The self-assembled nanoparticles of PTX prodrugs were formed by connecting PTX with different chemotherapeutic drugs or photosensitizers. This strategy effectively overcame drug resistance and exhibited enhanced antitumor effects in vivo with low toxicity. Second, using a combination of bionic and prodrug technologies, a cancer cell-targeted drug delivery system based on mesoporous silica nanoparticles (MSNs) encapsulated by cancer cell membranes was designed. This system demonstrated synergistically enhanced anticancer effects in cellular experiments. In summary, this thesis has provided new ideas for improving the shortcomings of traditional combined chemotherapy and photodynamic therapy, realizing the synchronous delivery and controlled release of different antitumor drugs, enhancing the synergy of drugs, and improving the efficacy of inhibiting tumor proliferation and metastasis.Cancer är en utmanande sjukdom att bota. Nuvarande behandlingsmetoder inkluderar främst kemoterapi och fototerapi. Kemoterapiläkemedel orsakar fortfarande stort lidande för cancerpatienter på grund av sin höga toxicitet och systemiska distribution. Dessutom är den kliniska effekten av behandling med ett enda läkemedel begränsad på grund av den komplexa patogenesen av maligna tumörer samt multiläkemedelsresistens som ofta uppvisas av tumörceller. För att hantera dessa utmaningar används i stor utsträckning kombinationsterapi med flera läkemedel eller flera behandlingsmetoder för att behandla olika maligniteter. Parallellt har den snabba utvecklingen av nanoteknik främjat tillämpningen av nanoläkemedel i kombinationskemoterapi. Även om nanoläkemedel kan öka läkemedelskoncentrationen i tumörområdet, utgör läkemedlsrester i levern och njurarna fortfarande ett hot mot människors hälsa. Prodroger är farmakologiskt inaktiva läkemedel eller föreningar som metaboliseras till farmakologiskt aktiva läkemedel efter intag av människokroppen. Strategier för behandling med prodroger har blivit en explorativ inriktning för att hantera biverkningarna av kemoterapi. Nanomedicin-baserade prodroger kan framställas för att förbättra målsökningseffektiviteten genom att använda cancercellsmålsökande ligander och endast friätta den aktiva substansen som en respons på tumörens lätt sura och reducerande mikromiljö genom att använda olika kemiska bindningar, vilket i sin tur kan förbättra antitumöreffekten och minska de toxiska biverkningarna på friska vävnader. I detta examensarbete designade vi prodrog-baserade nanomaterial och studerade antitumöreffekterna av prodrogerna med hjälp av olika läkemedelsadministrationssystem. Först syntetiserades reduktionskänsliga paklitaxel (PTX) prodroger för att uppnå synergistisk behandling av cancerkemoterapi och fotodynamisk terapi för att behandla cancerceller. De självaggregerande nanopartiklarna av PTX-prodroger bildades genom att koppla PTX med olika kemoterapeutiska läkemedel eller fotosensibilisatorer. Denna strategi övervann effektivt läkemedelsresistens och uppvisade förbättrade antitumöreffekter in vivo med låg toxicitet. Sedan designades med hjälp av en kombination av bionisk och prodrugteknologi ett cancercellriktat läkemedelslevereringssystem baserat på mesoporösa kiseldioxidnanopartiklar inkapslade av cancercellmembran. Detta system visade synergistiskt förbättrade anticancereffekter i cellulära experiment. Sammanfattningsvis har denna avhandling kommit fram med nya idéer för att förbättra bristerna i traditionell kombinationskemoterapi och fotodynamisk terapi, samt förverkliga den samtidiga tillförseln och kontrollerade frisättningen av olika antitumörläkemedel, och därmed förbättra synergin mellan läkemedlen och hämning av tumörproliferation och metastasering

Interactive Attention Networks for Aspect-Level Sentiment Classification

Aspect-level sentiment classification aims at identifying the sentiment polarity of specific target in its context. Previous approaches have realized the importance of targets in sentiment classification and developed various methods with the goal of precisely modeling their contexts via generating target-specific representations. However, these studies always ignore the separate modeling of targets. In this paper, we argue that both targets and contexts deserve special treatment and need to be learned their own representations via interactive learning. Then, we propose the interactive attention networks (IAN) to interactively learn attentions in the contexts and targets, and generate the representations for targets and contexts separately. With this design, the IAN model can well represent a target and its collocative context, which is helpful to sentiment classification. Experimental results on SemEval 2014 Datasets demonstrate the effectiveness of our model.Comment: Accepted by IJCAI 201

Robust Principal Component Analysis?

This paper is about a curious phenomenon. Suppose we have a data matrix, which is the superposition of a low-rank component and a sparse component. Can we recover each component individually? We prove that under some suitable assumptions, it is possible to recover both the low-rank and the sparse components exactly by solving a very convenient convex program called Principal Component Pursuit; among all feasible decompositions, simply minimize a weighted combination of the nuclear norm and of the L1 norm. This suggests the possibility of a principled approach to robust principal component analysis since our methodology and results assert that one can recover the principal components of a data matrix even though a positive fraction of its entries are arbitrarily corrupted. This extends to the situation where a fraction of the entries are missing as well. We discuss an algorithm for solving this optimization problem, and present applications in the area of video surveillance, where our methodology allows for the detection of objects in a cluttered background, and in the area of face recognition, where it offers a principled way of removing shadows and specularities in images of faces

Stable Principal Component Pursuit

In this paper, we study the problem of recovering a low-rank matrix (the principal components) from a high-dimensional data matrix despite both small entry-wise noise and gross sparse errors. Recently, it has been shown that a convex program, named Principal Component Pursuit (PCP), can recover the low-rank matrix when the data matrix is corrupted by gross sparse errors. We further prove that the solution to a related convex program (a relaxed PCP) gives an estimate of the low-rank matrix that is simultaneously stable to small entrywise noise and robust to gross sparse errors. More precisely, our result shows that the proposed convex program recovers the low-rank matrix even though a positive fraction of its entries are arbitrarily corrupted, with an error bound proportional to the noise level. We present simulation results to support our result and demonstrate that the new convex program accurately recovers the principal components (the low-rank matrix) under quite broad conditions. To our knowledge, this is the first result that shows the classical Principal Component Analysis (PCA), optimal for small i.i.d. noise, can be made robust to gross sparse errors; or the first that shows the newly proposed PCP can be made stable to small entry-wise perturbations.Comment: 5-page paper submitted to ISIT 201