Exponentially Improving the Complexity of Simulating the Weisfeiler-Lehman Test with Graph Neural Networks

Recent work shows that the expressive power of Graph Neural Networks (GNNs) in distinguishing non-isomorphic graphs is exactly the same as that of the Weisfeiler-Lehman (WL) graph test. In particular, they show that the WL test can be simulated by GNNs. However, those simulations involve neural networks for the 'combine' function of size polynomial or even exponential in the number of graph nodes $n$, as well as feature vectors of length linear in $n$. We present an improved simulation of the WL test on GNNs with \emph{exponentially} lower complexity. In particular, the neural network implementing the combine function in each node has only a polylogarithmic number of parameters in $n$, and the feature vectors exchanged by the nodes of GNN consists of only $O(\log n)$ bits. We also give logarithmic lower bounds for the feature vector length and the size of the neural networks, showing the (near)-optimality of our construction.Comment: 22 pages,5 figures, accepted at NeurIPS 202

Sublinear time algorithms for earth mover's distance

We study the problem of estimating the Earth Mover’s Distance (EMD) between probability distributions when given access only to samples of the distributions. We give closeness testers and additive-error estimators over domains in [0, 1][superscript d], with sample complexities independent of domain size – permitting the testability even of continuous distributions over infinite domains. Instead, our algorithms depend on other parameters, such as the diameter of the domain space, which may be significantly smaller. We also prove lower bounds showing the dependencies on these parameters to be essentially optimal. Additionally, we consider whether natural classes of distributions exist for which there are algorithms with better dependence on the dimension, and show that for highly clusterable data, this is indeed the case. Lastly, we consider a variant of the EMD, defined over tree metrics instead of the usual l 1 metric, and give tight upper and lower bounds

Testing non-uniform k-wise independent distributions over product spaces (extended abstract)

A distribution D over Σ1× ⋯ ×Σ n is called (non-uniform) k-wise independent if for any set of k indices {i 1, ..., i k } and for any z1zki1ik, PrXD[Xi1Xik=z1zk]=PrXD[Xi1=z1]PrXD[Xik=zk]. We study the problem of testing (non-uniform) k-wise independent distributions over product spaces. For the uniform case we show an upper bound on the distance between a distribution D from the set of k-wise independent distributions in terms of the sum of Fourier coefficients of D at vectors of weight at most k. Such a bound was previously known only for the binary field. For the non-uniform case, we give a new characterization of distributions being k-wise independent and further show that such a characterization is robust. These greatly generalize the results of Alon et al. [1] on uniform k-wise independence over the binary field to non-uniform k-wise independence over product spaces. Our results yield natural testing algorithms for k-wise independence with time and sample complexity sublinear in terms of the support size when k is a constant. The main technical tools employed include discrete Fourier transforms and the theory of linear systems of congruences.National Science Foundation (U.S.) (NSF grant 0514771)National Science Foundation (U.S.) (grant 0728645)National Science Foundation (U.S.) (Grant 0732334)Marie Curie International Reintegration Grants (Grant PIRG03-GA-2008-231077)Israel Science Foundation (Grant 1147/09)Israel Science Foundation (Grant 1675/09)Massachusetts Institute of Technology (Akamai Presidential Fellowship

Cadherin–catenin expression in primary colorectal cancer: a survival analysis

Both cell adhesion and cell signalling events are mediated by components of the cadherin-catenin complex. Loss of expression of the components of this complex have been shown to correlate with invasive behaviour in many tumour types although their exact role in colorectal cancer remains unclear. Immunohistochemical analysis of the expression of components of the cadherin-catenin complex in colorectal cancers from 60 patients was undertaken. Loss of memberanous expression of E-cadherin, alpha-catenin and beta-catenin was demonstrated in 52%, 85% and 40% of tumours respectively. Focal nuclear expression of beta-catenin ( 75% of tumour cells per section) was seen in 11 (18%) tumours. Loss of membranous alpha-catenin expression significantly correlated with tumour de-differentiation (P = 0.009). There was a trend towards an association between advanced tumour stage and loss of membranous expression of alpha-catenin or beta-catenin, although these associations were not statistically significant. Univariate analysis revealed that advanced Dukes' stage, tumour de-differentiation, loss of membranous beta-catenin expression, cytoplasmic beta-catenin expression and widespread nuclear expression of beta-catenin all correlated with short survival following apparently curative resection of the primary tumour. However, only Dukes' stage (P = 0.002), tumour grade (P = 0.02) and widespread nuclear expression of beta-catenin (P = 0.002) were independent predictors of short survival. Disturbed growth signalling events in colorectal tumours are thought to result in nuclear accumulation of beta-catenin. Consequently, tumours with widespread nuclear expression of beta-catenin are likely to have severely abnormal growth characteristics, and which therefore might be predictive of short survival in these patients

Reduction in membranous expression of β-catenin and increased cytoplasmic E-cadherin expression predict poor survival in gastric cancer

β-catenin, a component of the E-cadherin–catenin cell adhesion complex, also plays a separate intracellular signalling role, interacting with APC protein. Intracellular accumulation of β-catenin is common in colorectal neoplasia. β-catenin abnormalities are associated with poor survival in gastric cancer, but previous studies do not differentiate between membrane-associated and intracellular β-catenin. In this study we aimed to determine which type of expression abnormalities for E-cadherin, β-catenin and α-catenin correlate with clinico-pathological features and survival in gastric cancer. Immunoperoxidase staining of paraffin-embedded sections from 40 gastric cancers was performed for E-cadherin, α- and β-catenins using microwave unmasking and an avidin–biotin technique. Clinical data were obtained from case records and cancer registry records. Reduced membranous expression of β-catenin occurred in 10/12 (83%) diffuse and 8/28 (29%) intestinal tumours (P = 0.0014), and was associated with poor differentiation (P = 0.0015) and short survival (P = 0.032), but not with age, sex, tumour size or nodal status. Nuclear expression of β-catenin was uncommon; cytoplasmic expression was observed in 13/40 cases (33%) but did not correlate with histology, tumour grade or survival. Reduced E-cadherin membrane expression was associated with lymph node metastasis (P = 0.02). Neither E-cadherin or α-catenin expression correlated with survival. Reduced membranous expression of β-catenin predicts poor prognosis in gastric cancer, whilst ectopic intracellular expression is relatively rare. The apparent differences in β-catenin expression from those found in colon cancer merit further study. © 1999 Cancer Research Campaig

Genetic Mechanisms in Apc-Mediated Mammary Tumorigenesis

Many components of Wnt/β-catenin signaling pathway also play critical roles in mammary tumor development, yet the role of the tumor suppressor gene APC (adenomatous polyposis coli) in breast oncongenesis is unclear. To better understand the role of Apc in mammary tumorigenesis, we introduced conditional Apc mutations specifically into two different mammary epithelial populations using K14-cre and WAP-cre transgenic mice that express Cre-recombinase in mammary progenitor cells and lactating luminal cells, respectively. Only the K14-cre–mediated Apc heterozygosity developed mammary adenocarcinomas demonstrating histological heterogeneity, suggesting the multilineage progenitor cell origin of these tumors. These tumors harbored truncation mutation in a defined region in the remaining wild-type allele of Apc that would retain some down-regulating activity of β-catenin signaling. Activating mutations at codons 12 and 61 of either H-Ras or K-Ras were also found in a subset of these tumors. Expression profiles of acinar-type mammary tumors from K14-cre; ApcCKO/+ mice showed luminal epithelial gene expression pattern, and clustering analysis demonstrated more correlation to MMTV-neu model than to MMTV-Wnt1. In contrast, neither WAP-cre–induced Apc heterozygous nor homozygous mutations resulted in predisposition to mammary tumorigenesis, although WAP-cre–mediated Apc deficiency resulted in severe squamous metaplasia of mammary glands. Collectively, our results suggest that not only the epithelial origin but also a certain Apc mutations are selected to achieve a specific level of β-catenin signaling optimal for mammary tumor development and explain partially the colon- but not mammary-specific tumor development in patients that carry germline mutations in APC

Authenticated LSM Trees with Minimal Trust

In the age of user-generated contents, the workloads imposed on information-security infrastructures become increasingly write-intensive. How- ever, existing security protocols, specifically authenticated data structures (ADSs), are historically designed based on update-in-place data structures and incur overhead when serving write-intensive workloads. In this work, we present LPAD (Log-structured Persistent Authenticated Directory), a new ADS protocol designed uniquely based on the log-structured merge trees (LSM trees) which recently gained popularity in the design of modern storage systems. On the write path, LPAD supports streaming, non-interactive updates with constant proof from trusted data owners. On the read path, LPAD supports point queries over the dynamic dataset with polynomial proof. The key to enable this efficiency is a verifiable reorganization operation, called verifiable merge, in LPAD. Verifiable merge is secured by the execution in an enclave of trusted execution environments (TEE). To minimize the trusted computing base (TCB), LPAD places the code related to verifiable merge in enclave, and nothing else. Our implementation of LPAD on Google LevelDB codebase and on Intel SGX shows that the TCB is reduced by 20 times: The enclave size of LPAD is one thousand code lines out of more than twenty thousands code lines of a vanilla LevelDB. Under the YCSB workloads, LPAD improves the performance by an order of magnitude compared with that of existing update-in-place ADSs

Role of Wnt canonical pathway in hematological malignancies

Wnt canonical signaling pathway plays a diverse role in embryonic development and maintenance of organs and tissues in adults. It has been observed that Wnt/β-catenin signaling pathway is involved in the pathogenesis of many carcinomas. Moreover, Wnt/β-catenin pathway has been revealed to be associated with angiogenesis. Wnt canonical pathway signaling has great potential as a therapeutic target. It has been disclosed that some hematological malignancies, such as chronic lymphocytic leukemia, mantle cell lymphoma, may occur partly due to the constitutive activation of Wnt canonical signaling pathway. This review will summarize the latest development in Wnt canonical signaling pathway and its roles in tumorigenesis and angiogenesis

NFV, an HIV-1 protease inhibitor, induces growth arrest, reduced Akt signalling, apoptosis and docetaxel sensitisation in NSCLC cell lines

HIV-1 protease inhibitor (PI), nelfinavir (NFV) induced growth arrest and apoptosis of NCI-H460 and -H520, A549, EBC-1 and ABC-1 non-small-cell lung cancer (NSCLC) cells in association with upregulation of p21waf1, p27 kip1 and p53, and downregulation of Bcl-2 and matrix metalloproteinase (MMP)-2 proteins. We found that NFV blocked Akt signalling in these cells as measured by Akt kinase assay with glycogen synthase kinase-3α/β (GSK-3α/β) as a substrate. To explore the role of Akt signalling in NFV-mediated growth inhibition of NSCLC cells, we blocked this signal pathway by transfection of Akt small interfering RNA (siRNA) in these cells; transient transfection of Akt siRNA in NCI-H460 cells decreased the level of Bcl-2 protein and slowed their proliferation compared to the nonspecific siRNA-transfected cells. Conversely, forced-expression of Akt partially reversed NFV-mediated growth inhibition of these cells, suggesting that Akt may be a molecular target of NFV in NSCLC cells. Also, we found that inhibition of Akt signalling by NFV enhanced the ability of docetaxel to inhibit the growth of NCI-H460 and -H520 cells, as measured by MTT assay. Importantly, NFV slowed the proliferation and induced apoptosis of NCI-H460 cells present as tumour xenografts in nude mice without adverse systemic effects. Taken together, this family of compounds might be useful for the treatment of individuals with NSCLC