A new algorithm for fast generalized DFTs

We give an new arithmetic algorithm to compute the generalized Discrete Fourier Transform (DFT) over finite groups $G$. The new algorithm uses $O(|G|^{\omega/2 + o(1)})$ operations to compute the generalized DFT over finite groups of Lie type, including the linear, orthogonal, and symplectic families and their variants, as well as all finite simple groups of Lie type. Here $\omega$ is the exponent of matrix multiplication, so the exponent $\omega/2$ is optimal if $\omega = 2$. Previously, "exponent one" algorithms were known for supersolvable groups and the symmetric and alternating groups. No exponent one algorithms were known (even under the assumption $\omega = 2$) for families of linear groups of fixed dimension, and indeed the previous best-known algorithm for $SL_2(F_q)$ had exponent $4/3$ despite being the focus of significant effort. We unconditionally achieve exponent at most $1.19$ for this group, and exponent one if $\omega = 2$. Our algorithm also yields an improved exponent for computing the generalized DFT over general finite groups $G$, which beats the longstanding previous best upper bound, for any $\omega$. In particular, assuming $\omega = 2$, we achieve exponent $\sqrt{2}$, while the previous best was $3/2$

The X-linked tumor suppressor TSPX downregulates cancer-drivers/oncogenes in prostate cancer in a C-terminal acidic domain dependent manner.

TSPX is a tumor suppressor gene located at Xp11.22, a prostate cancer susceptibility locus. It is ubiquitously expressed in most tissues but frequently downregulated in various cancers, including lung, brain, liver and prostate cancers. The C-terminal acidic domain (CAD) of TSPX is crucial for the tumor suppressor functions, such as inhibition of cyclin B/CDK1 phosphorylation and androgen receptor transactivation. Currently, the exact role of the TSPX CAD in transcriptional regulation of downstream genes is still uncertain. Using different variants of TSPX, we showed that overexpression of either TSPX, that harbors a CAD, or a CAD-truncated variant (TSPX[∆C]) drastically retarded cell proliferation in a prostate cancer cell line LNCaP, but cell death was induced only by overexpression of TSPX. Transcriptome analyses showed that TSPX or TSPX[∆C] overexpression downregulated multiple cancer-drivers/oncogenes, including MYC and MYB, in a CAD-dependent manner and upregulated various tumor suppressors in a CAD-independent manner. Datamining of transcriptomes of prostate cancer specimens in the Cancer Genome Atlas (TCGA) dataset confirmed the negative correlation between the expression level of TSPX and those of MYC and MYB in clinical prostate cancer, thereby supporting the hypothesis that the CAD of TSPX plays an important role in suppression of cancer-drivers/oncogenes in prostatic oncogenesis

Mechanisms of the Regulation of the Intestinal Na+/H+Exchanger NHE3

A major of Na+ absorptive process in the proximal part of intestine and kidney is electroneutral exchange of Na+ and H+ by Na+/H+ exchanger type 3 (NHE3). During the past decade, significant advance has been achieved in the mechanisms of NHE3 regulation. A bulk of the current knowledge on Na+/H+ exchanger regulation is based on heterologous expression of mammalian Na+/H+ exchangers in Na+/H+ exchanger deficient fibroblasts, renal epithelial, and intestinal epithelial cells. Based on the reductionist's approach, an understanding of NHE3 regulation has been greatly advanced. More recently, confirmations of in vitro studies have been made using animals deficient in one or more proteins but in some cases unexpected findings have emerged. The purpose of this paper is to provide a brief overview of recent progress in the regulation and functions of NHE3 present in the luminal membrane of the intestinal tract

Costs and benefits of wetland restoration of hydric cropland in Missouri: a preliminary assessment

This report presents a preliminary analysis of the benefits and costs of restoring hydric cropland sites to wetlands in Missouri. Potential social and private (landowner) benefits and costs were estimated for 25 sites in Livingston county and 23 sites in Linn county. Sites ranging in size from 36 to 68 acres were identified using a geographic information system. Social net benefits of wetland restoration for both counties were highest and positive ($431,248) with high benefits and low costs and negative and lowest (-$579,681) with low benefits and high costs. When wetland construction costs are fully subsidized and easement payments equal the opportunity cost of wetland restoration, private net benefits ranged from $629,905 (high landowner benefits) to$9,686 (low landowner benefits). It would be economically rational for a landowner to convert hydric cropland to wetland if the easement payment provided by the government is greater than or equal to the opportunity cost of wetland restoration, the cost of wetland construction is fully subsidized, and the income earned from the wetland equals or exceeds maintenance cost of the wetland. The first condition is likely to be satisfied for landowners who bid eligible cropland into the Wetland Reserve Program. The second condition would be satisfied under current cost-sharing provisions for wetlands. The third condition may or may not be satisfied.Project # G-2029-04 Agreement # 14-08-0001-G-2029-0

On Multidimensional and Monotone k-SUM

The well-known k-SUM conjecture is that integer k-SUM requires time Omega(n^{ceil{k/2}-o(1)}). Recent work has studied multidimensional k-SUM in F_p^d, where the best known algorithm takes time tilde O(n^{ceil{k/2}}). Bhattacharyya et al. [ICS 2011] proved a min(2^{Omega(d)},n^{Omega(k)}) lower bound for k-SUM in F_p^d under the Exponential Time Hypothesis. We give a more refined lower bound under the standard k-SUM conjecture: for sufficiently large p, k-SUM in F_p^d requires time Omega(n^{k/2-o(1)}) if k is even, and Omega(n^{ceil{k/2}-2k(log k)/(log p)-o(1)}) if k is odd. For a special case of the multidimensional problem, bounded monotone d-dimensional 3SUM, Chan and Lewenstein [STOC 2015] gave a surprising tilde O(n^{2-2/(d+13)}) algorithm using additive combinatorics. We show this algorithm is essentially optimal. To be more precise, bounded monotone d-dimensional 3SUM requires time Omega(n^{2-frac{4}{d}-o(1)}) under the standard 3SUM conjecture, and time Omega(n^{2-frac{2}{d}-o(1)}) under the so-called strong 3SUM conjecture. Thus, even though one might hope to further exploit the structural advantage of monotonicity, no substantial improvements beyond those obtained by Chan and Lewenstein are possible for bounded monotone d-dimensional 3SUM

PGL orbits in tree varieties

In this paper, we introduce tree varieties as a natural generalization of products of partial flag varieties. We study orbits of the PGL action on tree varieties. We characterize tree varieties with finitely many PGL orbits, generalizing a celebrated theorem of Magyar, Weyman and Zelevinsky. We give criteria that guarantee that a tree variety has a dense PGL orbit and provide many examples of tree varieties that do not have dense PGL orbits. We show that a triple of two-step flag varieties $F(k_1, k_2; n)^3$ has a dense PGL orbit if and only if $k_1 + k_2 \not= n$.Comment: 25 page

Testing the Task-Media Fit: The Effects of Task Equivocality on Social Presence of Mobile Video-Mediated Communication

Since social presence theory was introduced, many researchers have tried to apply it to various technology-mediated communication media, including E-Mail, videoconferencing, and instant messengers. Yet few researches have investigated the influence of mobile video-mediated communication (VMC) on the social presence despite prevalence in business practices. In this paper, a research model is developed to test the relationship between the mobile VMC (video telephony and video chatting) and the level of social presence. And the task equivocality, whether it’s an intellective task or a negotiation task, is also considered as moderating variables, based on the task-media fit proposition. Hence, mobile video chatting could be suggested as an alternative media of mobile video telephony for less equivocal informative tasks according to this study

A Neural Network Approach to Context-Sensitive Generation of Conversational Responses

We present a novel response generation system that can be trained end to end on large quantities of unstructured Twitter conversations. A neural network architecture is used to address sparsity issues that arise when integrating contextual information into classic statistical models, allowing the system to take into account previous dialog utterances. Our dynamic-context generative models show consistent gains over both context-sensitive and non-context-sensitive Machine Translation and Information Retrieval baselines.Comment: A. Sordoni, M. Galley, M. Auli, C. Brockett, Y. Ji, M. Mitchell, J.-Y. Nie, J. Gao, B. Dolan. 2015. A Neural Network Approach to Context-Sensitive Generation of Conversational Responses. In Proc. of NAACL-HLT. Pages 196-20