192,595 research outputs found
Fast Exact Algorithms Using Hadamard Product of Polynomials
Let C be an arithmetic circuit of poly(n) size given as input that computes a polynomial f in F[X], where X={x_1,x_2,...,x_n} and F is any field where the field arithmetic can be performed efficiently. We obtain new algorithms for the following two problems first studied by Koutis and Williams [Ioannis Koutis, 2008; Ryan Williams, 2009; Ioannis Koutis and Ryan Williams, 2016].
- (k,n)-MLC: Compute the sum of the coefficients of all degree-k multilinear monomials in the polynomial f.
- k-MMD: Test if there is a nonzero degree-k multilinear monomial in the polynomial f.
Our algorithms are based on the fact that the Hadamard product f o S_{n,k}, is the degree-k multilinear part of f, where S_{n,k} is the k^{th} elementary symmetric polynomial.
- For (k,n)-MLC problem, we give a deterministic algorithm of run time O^*(n^(k/2+c log k)) (where c is a constant), answering an open question of Koutis and Williams [Ioannis Koutis and Ryan Williams, 2016]. As corollaries, we show O^*(binom{n}{downarrow k/2})-time exact counting algorithms for several combinatorial problems: k-Tree, t-Dominating Set, m-Dimensional k-Matching.
- For k-MMD problem, we give a randomized algorithm of run time 4.32^k * poly(n,k). Our algorithm uses only poly(n,k) space. This matches the run time of a recent algorithm [Cornelius Brand et al., 2018] for k-MMD which requires exponential (in k) space.
Other results include fast deterministic algorithms for (k,n)-MLC and k-MMD problems for depth three circuits
Transfected poly(I:C) activates different dsRNA receptors leading to apoptosis or immunoadjuvant response in androgen-independent prostate cancer cells
Background: Castration-resistant prostate cancer (CRPC) is refractory to chemo-radiotherapy.
Results: Transfection of the synthetic analog of dsRNA poly(I:C) simultaneously stimulates apoptosis and IFN- expression
through different pathways in androgen-independent prostate cancer (PCa) cells.
Conclusion: Dual parallel pathways triggered by distinct receptors activate direct and immunologically mediated antitumor
effects in advanced PCa.
Significance: The proapoptotic/immunoadjuvant poly(I:C)-Lipofectamine complex may offer new therapeutic insights into CRPC
Exchangeable Variable Models
A sequence of random variables is exchangeable if its joint distribution is
invariant under variable permutations. We introduce exchangeable variable
models (EVMs) as a novel class of probabilistic models whose basic building
blocks are partially exchangeable sequences, a generalization of exchangeable
sequences. We prove that a family of tractable EVMs is optimal under zero-one
loss for a large class of functions, including parity and threshold functions,
and strictly subsumes existing tractable independence-based model families.
Extensive experiments show that EVMs outperform state of the art classifiers
such as SVMs and probabilistic models which are solely based on independence
assumptions.Comment: ICML 201
Noise-Resilient Group Testing with Order-Optimal Tests and Fast-and-Reliable Decoding
Group testing (GT) is the Boolean counterpart of compressed sensing and the
marketplace of new ideas for related problems such as cognitive radio and heavy
hitter. A GT scheme is considered good if it is nonadaptive, uses
tests, resists noise, can be decoded in
time, and makes nearly no mistakes. In this paper, we propose "Gacha GT", an
elementary, self-contained, and unified randomized scheme that, for the first
time, satisfies all criteria for a fairly large region of parameters, namely
when . Outside this parameter region, Gacha can be
specialized to outperform the state-of-the-art partial-recovery GTs,
exact-recovery GTs, and worst-case GTs.
The new idea that runs through this paper, using an analogy, is to ask every
person to break her -digit "phone number" into three -digit numbers ,
, and and write , , and on three pieces of
sticky notes, where is her "birthday". This way, one can sort the sticky
notes by birthday to reassemble the phone numbers. This birthday--number code
and other coded constructions can be stacked like a multipartite graph pyramid.
Gacha's encoder will synthesize the test results from the bottom up; and
Gacha's decoder will reassemble the phone numbers from the top down.Comment: 23 pages, 8 figure
- …