Approximate Sampling and Counting of Graphs with Near-Regular Degree Intervals

The approximate uniform sampling of graphs with a given degree sequence is a well-known, extensively studied problem in theoretical computer science and has significant applications, e.g., in the analysis of social networks. In this work we study an extension of the problem, where degree intervals are specified rather than a single degree sequence. We are interested in sampling and counting graphs whose degree sequences satisfy the degree interval constraints. A natural scenario where this problem arises is in hypothesis testing on social networks that are only partially observed. In this work, we provide the first fully polynomial almost uniform sampler (FPAUS) as well as the first fully polynomial randomized approximation scheme (FPRAS) for sampling and counting, respectively, graphs with near-regular degree intervals, in which every node $i$ has a degree from an interval not too far away from a given $d \in \N$. In order to design our FPAUS, we rely on various state-of-the-art tools from Markov chain theory and combinatorics. In particular, we provide the first non-trivial algorithmic application of a breakthrough result of Liebenau and Wormald (2017) regarding an asymptotic formula for the number of graphs with a given near-regular degree sequence. Furthermore, we also make use of the recent breakthrough of Anari et al. (2019) on sampling a base of a matroid under a strongly log-concave probability distribution. As a more direct approach, we also study a natural Markov chain recently introduced by Rechner, Strowick and M\"uller-Hannemann (2018), based on three simple local operations: Switches, hinge flips, and additions/deletions of a single edge. We obtain the first theoretical results for this Markov chain by showing it is rapidly mixing for the case of near-regular degree intervals of size at most one

Rapid mixing of the switch Markov chain for strongly stable degree sequences and 2-class joint degree matrices

The switch Markov chain has been extensively studied as the most natural Markov Chain Monte Carlo approach for sampling graphs with prescribed degree sequences. We use comparison arguments with other, less natural but simpler to analyze, Markov chains, to show that the switch chain mixes rapidly in two different settings. We first study the classic problem of uniformly sampling simple undirected, as well as bipartite, graphs with a given degree sequence. We apply an embedding argument, involving a Markov chain defined by Jerrum and Sinclair (TCS, 1990) for sampling graphs that almost have a given degree sequence, to show rapid mixing for degree sequences satisfying strong stability, a notion closely related to P-stability. This results in a much shorter proof that unifies the currently known rapid mixing results of the switch chain and extends them up to sharp characterizations of P-stability. In particular, our work resolves an open problem posed by Greenhill (SODA, 2015).Secondly, in order to illustrate the power of our approach, we study the problem of uniformly sampling graphs for which, in addition to the degree sequence, a joint degree distribution is given. Although the problem was formalized over a decade ago, and despite its practical significance in generating synthetic network topologies, small progress has been made on the random sampling of such graphs. The case of a single degree class reduces to sampling of regular graphs, but beyond this almost nothing is known. We fully resolve the case of two degree classes, by showing that the switch Markov chain is always rapidly mixing. Again, we first analyze an auxiliary chain for strongly stable instances on an augmented state space and then use an embedding argument.</p

On how CCN6 suppresses breast cancer growth and invasion

Living cells communicate with their microenvironment and exchange information through signaling pathways in order to carry out most biological processes. The CCN family of proteins has the ability to coordinate the extracellular and intracellular signaling pathways and epithelial-stromal cross-talks. CCN proteins have been shown to play roles in multiple processes including cancer, either as tumor suppressors or oncogenes. Particularly, loss of CCN6 expression has been reported in highly aggressive breast cancer types, especially in inflammatory breast cancer and breast cancer with axillary lymph node metastasis. Recent findings can better explain the biological relevance of CCN6 as a tumor suppressor protein in breast tumorigenesis. CCN6 loss triggers the process of epithelial to mesenchymal transition (EMT), which converts epithelial cells into migratory and invasive mesenchymal-like cells at least in part through modulation of IGF-1 receptor signaling pathway. Emerging data support the hypothesis that CCN6 also exerts growth factor independent functions, especially related to cell survival and anoikis resistance. Thus, our work provides new insights into the functions and mechanisms of tumor suppression exerted by CCN6 in the breast

Tubular carcinoma and grade 1 (well-differentiated) invasive ductal carcinoma: Comparison of flat epithelial atypia and other intra-epithelial lesions

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72926/1/j.1440-1827.2008.02280.x.pd

E-cadherin expression in primary carcinomas of the breast and its distant metastases

Abstract Introduction Aberrant expression of E-cadherin has been associated with the development of metastases in patients with breast cancer. Even though the expression of E-cadherin has been studied in primary breast tumors, little is known about its expression at the distant metastatic sites. We investigate the relationship between E-cadherin expression in primary breast carcinoma and their distant, non-nodal metastases. Methods Immunohistochemical analysis of E-cadherin was performed in tissues from 30 patients with primary invasive breast carcinoma and their distant metastases. E-cadherin expression was evaluated as normal or aberrant (decreased when compared with normal internal positive controls, or absent). Results Twenty-two (73%) invasive carcinomas were ductal, and eight (27%) were lobular. Of the primary invasive ductal carcinomas, 55% (12/22) had normal E-cadherin expression and 45% (10/22) had aberrant expression. All of the metastases expressed E-cadherin with the same intensity as (12 tumors) or with stronger intensity than (10 tumors) the corresponding primaries. Of the invasive lobular carcinomas, one of eight (12%) primary carcinomas and none of the metastases expressed E-cadherin in the cell membranes, but they accumulated the protein in the cytoplasm. Conclusion Aberrant E-cadherin expression is frequent in invasive ductal carcinomas that progress to develop distant metastases. Distant metastases consistently express E-cadherin, often more strongly than the primary tumor. Invasive lobular carcinomas have a different pattern of E-cadherin expression, suggesting a different role for E-cadherin in this form of breast carcinoma.http://deepblue.lib.umich.edu/bitstream/2027.42/112744/1/13058_2003_Article_652.pd

E-cadherin expression in primary carcinomas of the breast and its distant metastases

INTRODUCTION: Aberrant expression of E-cadherin has been associated with the development of metastases in patients with breast cancer. Even though the expression of E-cadherin has been studied in primary breast tumors, little is known about its expression at the distant metastatic sites. We investigate the relationship between E-cadherin expression in primary breast carcinoma and their distant, non-nodal metastases. METHODS: Immunohistochemical analysis of E-cadherin was performed in tissues from 30 patients with primary invasive breast carcinoma and their distant metastases. E-cadherin expression was evaluated as normal or aberrant (decreased when compared with normal internal positive controls, or absent). RESULTS: Twenty-two (73%) invasive carcinomas were ductal, and eight (27%) were lobular. Of the primary invasive ductal carcinomas, 55% (12/22) had normal E-cadherin expression and 45% (10/22) had aberrant expression. All of the metastases expressed E-cadherin with the same intensity as (12 tumors) or with stronger intensity than (10 tumors) the corresponding primaries. Of the invasive lobular carcinomas, one of eight (12%) primary carcinomas and none of the metastases expressed E-cadherin in the cell membranes, but they accumulated the protein in the cytoplasm. CONCLUSION: Aberrant E-cadherin expression is frequent in invasive ductal carcinomas that progress to develop distant metastases. Distant metastases consistently express E-cadherin, often more strongly than the primary tumor. Invasive lobular carcinomas have a different pattern of E-cadherin expression, suggesting a different role for E-cadherin in this form of breast carcinoma

CCN6 Knockdown Disrupts Acinar Organization of Breast Cells in Three-dimensional Cultures through Up-regulation of Type III TGF-β Receptor

AbstractWhile normal cells in the human breast are organized into acinar structures, disruption of the acinar architecture is a hallmark of cancer. In a three-dimensional model of morphogenesis, we show that down-regulation of the matrix-associated tumor suppressor protein CCN6 (WNT1-inducible-signaling pathway protein 3) disrupts breast epithelial cell polarity and organization into acini through up-regulation of the type III transforming growth factor-β receptor (TβRIII or betaglycan). Down-regulation of CCN6 in benign breast cells led to loss of tissue polarity and resulted in cellular disorganization with loss of α6 integrin-rich basement membrane and the basolateral polarity protein E-cadherin. Silencing of TβRIII with shRNA and siRNA rescued the ability of breast epithelial cells to form polarized acinar structures with reduced matrix invasion and restored the correct expression of α6 integrin and E-cadherin. Conversely, CCN6 overexpression in aggressive breast cancer cells reduced TβRIII in vitro and in a xenograft model of CCN6 overexpression. The relevance of our studies to human breast cancer is highlighted by the finding that CCN6 protein levels are inversely associated with TβRIII protein in 64%of invasive breast carcinomas. These results reveal a novel function of the matricellular protein CCN6 and establish a mechanistic link between CCN6 and TβRIII in maintaining acinar organization in the breast

Endoscopic and histological patchiness in treated ulcerative colitis

Traditionally, contiguous distribution of inflammation (endoscopic and histological) with rectal involvement is thought to be important in distinguishing ulcerative colitis (UC) from Crohn's disease of the colon. Little long-term data are available that prove whether this rule holds during the course of disease as it is modified by time and treatment. The aim of this study was to investigate the prevalence of endoscopic and histological patchiness and rectal sparing in treated UC over time and to correlate these findings with treatment at the time of endoscopy. Methods : Patients with well-established UC who underwent sequential colonoscopy or flexible sigmoidoscopy with biopsies were included in this study. Patients’ medical records including endoscopy/biopsy reports and clinical status/symptoms/treatment at the time of endoscopy were reviewed retrospectively. Results : A total of 32 patients (14 men, 18 women; median age, 45 yr; median UC duration, 15 yr) underwent 175 sequential endoscopies with biopsies (161 colonoscopies, 14 sigmoidoscopies; median, five endoscopies per patient; range, 3–10). Endoscopic and/or histological patchiness was present in 20 of 175 (11%) sequential endoscopies with biopsies over time from 12 of 32 (38%) patients. Endoscopic and/or histological rectal sparing was present in 27 of 175 (15%) of sequential endoscopies with biopsies over time from 14 of 32 (44%) patients. Seven patients had both patchiness and rectal sparing. Therefore, in 47 (27%) follow-up endoscopies in 19 (59%) patients, there was either patchy disease, rectal sparing, or both sometime during the course of disease with treatment. There was no significant difference in treatment, including steroid use and rectal therapy, between those with patchiness and/or rectal sparing and those without. Conclusions : Contrary to traditional teaching, endoscopic and histological patchiness of inflammation and rectal sparing are common during the course of disease in treated UC and seem to be unrelated to specific therapy.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/74642/1/j.1572-0241.1999.01533.x.pd

Readiness of Quantum Optimization Machines for Industrial Applications

There have been multiple attempts to demonstrate that quantum annealing and, in particular, quantum annealing on quantum annealing machines, has the potential to outperform current classical optimization algorithms implemented on CMOS technologies. The benchmarking of these devices has been controversial. Initially, random spin-glass problems were used, however, these were quickly shown to be not well suited to detect any quantum speedup. Subsequently, benchmarking shifted to carefully crafted synthetic problems designed to highlight the quantum nature of the hardware while (often) ensuring that classical optimization techniques do not perform well on them. Even worse, to date a true sign of improved scaling with the number of problem variables remains elusive when compared to classical optimization techniques. Here, we analyze the readiness of quantum annealing machines for real-world application problems. These are typically not random and have an underlying structure that is hard to capture in synthetic benchmarks, thus posing unexpected challenges for optimization techniques, both classical and quantum alike. We present a comprehensive computational scaling analysis of fault diagnosis in digital circuits, considering architectures beyond D-wave quantum annealers. We find that the instances generated from real data in multiplier circuits are harder than other representative random spin-glass benchmarks with a comparable number of variables. Although our results show that transverse-field quantum annealing is outperformed by state-of-the-art classical optimization algorithms, these benchmark instances are hard and small in the size of the input, therefore representing the first industrial application ideally suited for testing near-term quantum annealers and other quantum algorithmic strategies for optimization problems.Comment: 22 pages, 12 figures. Content updated according to Phys. Rev. Applied versio

Contamination Level of Staphylococcus spp. in Raw Goat Milk and Associated Risk Factors

This study was aimed to investigate the presence of pathogenic bacteria in raw goat milk by using Staphylococcus spp. as indicator bacteria, and also to evaluate the potential risk factors associated with them. Information regarding potential risk factors was collected by questionnaire. The conventional bacteriological method for bacterial isolation and the indirect test (California Mastitis Test (CMT)) for determining udder inflammation status were employed. A sample size of 300 udder halves milk samples from three commercial dairy goat farms in the Bogor District, West Java Province, Indonesia were investigated for counts and prevalence of indicator bacteria. Ten potential risk factors were also evaluated in relation to counts and prevalence of indicator bacteria. The results showed that the median value of indicator bacterial count from overall udder-half milk samples was 3.00 log cfu/ml. The indicator bacterial count from udder-half milk samples was significantly different (P < 0.05) among farms. Overall prevalence of Staphylococcus spp. was 78.7%. As one of potential risk factors, udder inflammation status was found to be risk factor for Staphylococcus spp. contamination in milk. Udders with inflammation had significant association and a higher chance of having contaminated samples by Staphylococcus spp. as compared to udders without inflammation. Additionally, according to these study results, CMT can be used as an effective, reliable, cheap and “farm and farmer friendly test" for screening test of intramammary infection (IMI) or sub clinical mastitis in dairy goats. Key words: goat milk, Staphylococcus spp., prevalence, risk factor, California Mastitis Tes