Flat Cyclotomic Polynomials: A New Approach

We build a new theory for analyzing the coefficients of any cyclotomic polynomial by considering it as a gcd of simpler polynomials. Using this theory, we generalize a result known as periodicity and provide two new families of flat cyclotomic polynomials. One, of order 3, was conjectured by Broadhurst: $\Phi_{pqr}(x)$ is flat where $p<q<r$ are primes and there is a positive integer $w$ such that $r\equiv\pm w\pmod{pq}$, $p\equiv1\pmod w$ and $q\equiv1\pmod{wp}$. The other is the first general family of order 4: $\Phi_{pqrs}(x)$ is flat for primes $p,q,r,s$ where $q\equiv-1\pmod p$, $r\equiv\pm1\pmod{pq}$, and $s\equiv\pm1\pmod{pqr}$. Finally, we prove that the natural extension of this second family to order 5 is never flat, suggesting that there are no flat cyclotomic polynomials of order 5.Comment: 52 pages; to be submitted to International Journal of Number Theor

Dimensionality Reduction for k-Means Clustering and Low Rank Approximation

We show how to approximate a data matrix $\mathbf{A}$ with a much smaller sketch $\mathbf{\tilde A}$ that can be used to solve a general class of constrained k-rank approximation problems to within $(1+\epsilon)$ error. Importantly, this class of problems includes $k$-means clustering and unconstrained low rank approximation (i.e. principal component analysis). By reducing data points to just $O(k)$ dimensions, our methods generically accelerate any exact, approximate, or heuristic algorithm for these ubiquitous problems. For $k$-means dimensionality reduction, we provide $(1+\epsilon)$ relative error results for many common sketching techniques, including random row projection, column selection, and approximate SVD. For approximate principal component analysis, we give a simple alternative to known algorithms that has applications in the streaming setting. Additionally, we extend recent work on column-based matrix reconstruction, giving column subsets that not only `cover' a good subspace for \bv{A}, but can be used directly to compute this subspace. Finally, for $k$-means clustering, we show how to achieve a $(9+\epsilon)$ approximation by Johnson-Lindenstrauss projecting data points to just $O(\log k/\epsilon^2)$ dimensions. This gives the first result that leverages the specific structure of $k$-means to achieve dimension independent of input size and sublinear in $k$

Making the Academic Writing Process Explicit for Doctoral Students in the Social Sciences

The purpose of this article is to clarify the academic writing process and stages of publication for novice scholars. With doctoral student mentorship being highly dependent on relationships with faculty mentors, the quality and type of mentorship received varies widely. We designed this article to provide a shared starting point for new scholars trying to navigate the writing and publication process. We use our experiences as three newly tenured faculty members to provide some guidance for students. Additionally, this article adds to the existing body of knowledge on the academic writing process by bringing some hidden curriculum and norms to the forefront and making the information available to all students. Article highlights include four areas of focus of academic publishing: (a) the presentation to publication process; (b) journal choice and preparing for journal submission; (c) revision as a communal process; and (d) the journal response. Within this article, we have recommended several places where new scholars can make decisions ranging from where to submit papers, who and how to ask for help, and ways that they can respond to reviewers

Making the Academic Writing Process Explicit for Doctoral Students in the Social Sciences

The purpose of this article is to clarify the academic writing process and stages of publication for novice scholars. With doctoral student mentorship being highly dependent on relationships with faculty mentors, the quality and type of mentorship received varies widely. We designed this article to provide a shared starting point for new scholars trying to navigate the writing and publication process. We use our experiences as three newly tenured faculty members to provide some guidance for students. Additionally, this article adds to the existing body of knowledge on the academic writing process by bringing some hidden curriculum and norms to the forefront and making the information available to all students. Article highlights include four areas of focus of academic publishing: (a) the presentation to publication process; (b) journal choice and preparing for journal submission; (c) revision as a communal process; and (d) the journal response. Within this article, we have recommended several places where new scholars can make decisions ranging from where to submit papers, who and how to ask for help, and ways that they can respond to reviewers

Improved Nonrelapse Mortality and Infection Rate with Lower Dose of Antithymocyte Globulin in Patients Undergoing Reduced-Intensity Conditioning Allogeneic Transplantation for Hematologic Malignancies

We sought to reduce the risk of infectious complications and nonrelapse mortality (NRM) associated with the use of antithymocyte globulin (ATG) without compromising control of acute graft-versus-host disease (aGVHD) in patients undergoing reduced-intensity conditioning (RIC) transplantation. As part of an ongoing quality improvement effort, we lowered the dose of rabbit ATG from 7.5 mg/kg of ATG (R-ATG) (n = 39) to 6.0 mg/kg of ATG (r-ATG) (n = 33) in association with fludarabine (Flu) and busulfan (BU) RIC transplantation and then monitored patients for adverse events, relapse, and survival. Of the 72 mostly high risk (82%) patients studied, 89% received unrelated donor allografts, 25% of which were HLA-mismatched. No differences in posttransplantation full donor-cell chimerism rates were observed between the 2 ATG-dose groups (P > .05). When R-ATG versus r-ATG patients were compared, we observed no significant difference in the cumulative incidence of grade II-IV aGVHD (32% versus 27%; P = .73) or grade III-IV aGVHD (23% versus 11%; P = .28). However, the r-ATG group had significantly less cytomegalovirus (CMV) reactivation (64% versus 30%; P = .005) and bacterial infections (56% versus 18%; P = .001), a better 1-year cumulative incidence of NRM (18% versus 3%; P = .03), and a trend for better 1-year overall survival (OS) (64% versus 84%; P = .07) compared to R-ATG patients. A seemingly modest reduction in the dose of rabbit ATG did not compromise control of aGVHD or achievement of donor chimerism, but led to a significant decrease in the risk of serious infections and NRM in high-risk RIC allograft recipients

A single cell characterisation of human embryogenesis identifies pluripotency transitions and putative anterior hypoblast centre.

Following implantation, the human embryo undergoes major morphogenetic transformations that establish the future body plan. While the molecular events underpinning this process are established in mice, they remain unknown in humans. Here we characterise key events of human embryo morphogenesis, in the period between implantation and gastrulation, using single-cell analyses and functional studies. First, the embryonic epiblast cells transition through different pluripotent states and act as a source of FGF signals that ensure proliferation of both embryonic and extra-embryonic tissues. In a subset of embryos, we identify a group of asymmetrically positioned extra-embryonic hypoblast cells expressing inhibitors of BMP, NODAL and WNT signalling pathways. We suggest that this group of cells can act as the anterior singalling centre to pattern the epiblast. These results provide insights into pluripotency state transitions, the role of FGF signalling and the specification of anterior-posterior axis during human embryo development

Addition of Infliximab to Standard Acute Graft-versus-Host Disease Prophylaxis following Allogeneic Peripheral Blood Cell Transplantation

Infliximab, a chimeric monoclonal antibody (mAb) against tumor necrosis factor (TNF)-α, has shown activity against steroid refractory acute graft-versus-host disease (aGVHD). We conducted a prospective trial of infliximab for the prophylaxis of aGVHD. Patients older than 20 years undergoing myeloablative allogeneic stem cell transplantation (SCT) for hematologic malignancies were eligible. GVHD prophylaxis consisted of infliximab given 1 day prior to conditioning and then on days 0, +7, +14, +28, and +42, together with standard cyclosporine (CSA) and methotrexate (MTX). Nineteen patients with a median age of 53 years were enrolled. All patients received peripheral blood allografts from matched sibling (n = 14) or unrelated donors (n = 5). Results were compared with a matched historic control group (n = 30) treated contemporaneously at our institution. The cumulative incidences of grades II-IV aGVHD in the infliximab and control groups were 36.8% and 36.6%, respectively (P = .77). Rates of chronic GVHD were 78% and 61%, respectively (P = .22). Significantly more bacterial and invasive fungal infections were observed in the infliximab group (P = .01 and P = .02, respectively). Kaplan-Meier estimates of 2-year overall survival (OS) and progression free survival (PFS) for patients receiving infliximab were 42% and 36%, respectively. The corresponding numbers for patients in the control group were 46% and 43%, respectively. The addition of infliximab to standard GVHD prophylaxis did not lower the risk of GVHD and was associated with an increased risk of bacterial and invasive fungal infections