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Discrete Computational Geometry, 56(4):882–909, June 2016. doi:10.1007/ s00454-016-9793-3.  Daniel Dadush and Sophie Huiberts. A friendly smoothed analysis of the simplex method. ... Huiberts∗∗ Galyna Livshyts†† Centrum Wiskunde & Informatica Georgia Institute of Technology arXiv ...arXiv:2112.13027v1 fatcat:6c7ucu6xvnh2npl4tu3wgcmw4y
vol d (\scrB d 2 ) \surd 2\pi d \leq e (dc 2 log n)/2 \biggl( \surd e c \surd log n \biggr) d \leq e (dc 2 log n)/2 , (3.19) STOC18-486 DANIEL DADUSH AND SOPHIE HUIBERTS where we ...doi:10.1137/18m1197205 fatcat:gbnr52kzwnam5haonc7z7co5mi
We give a simple and natural method for computing approximately optimal solutions for minimizing a convex function f over a convex set K given by a separation oracle. Our method utilizes the Frank–Wolfe algorithm over the cone of valid inequalities of K and subgradients of f. Under the assumption that f is L-Lipschitz and that K contains a ball of radius r and is contained inside the origin centered ball of radius R, using O((RL)^2/ε^2·R^2/r^2) iterations and calls to the oracle, our mainarXiv:2011.08557v2 fatcat:kmcsb2za4rdhbf3jpqct6bivbu
more »... cle, our main method outputs a point x ∈ K satisfying f(x) ≤ε + min_z ∈ K f(z). Our algorithm is easy to implement, and we believe it can serve as a useful alternative to existing cutting plane methods. As evidence towards this, we show that it compares favorably in terms of iteration counts to the standard LP based cutting plane method and the analytic center cutting plane method, on a testbed of combinatorial, semidefinite and machine learning instances.
Explaining the excellent practical performance of the simplex method for linear programming has been a major topic of research for over 50 years. One of the most successful frameworks for understanding the simplex method was given by Spielman and Teng (JACM '04), who developed the notion of smoothed analysis. Starting from an arbitrary linear program with d variables and n constraints, Spielman and Teng analyzed the expected runtime over random perturbations of the LP (smoothed LP), wheredoi:10.1145/3188745.3188826 dblp:conf/stoc/DadushH18 fatcat:d2g3rg3zcrdlxnlkhvhbwz5svi
more »... ed LP), where variance σ 2 Gaussian noise is added to the LP data. In particular, they gave a two-stage shadow vertex simplex algorithm which uses an expected O(d 55 n 86 (1+σ −30 )) number of simplex pivots to solve the smoothed LP. Their analysis and runtime was substantially improved by Deshpande and Spielman (FOCS '05) and later Vershynin (SICOMP '09). The fastest current algorithm, due to Vershynin, solves the smoothed LP using an expected O(d 3 log 3 n σ −4 + d 9 log 7 n) number of pivots, improving the dependence on n from polynomial to logarithmic. While the original proof of Spielman and Teng has now been substantially simplified, the resulting analyses are still quite long and complex and the parameter dependencies far from optimal. In this work, we make substantial progress on this front, providing an improved and simpler analysis of shadow simplex methods, where our main algorithm requires an expected O(d 2 log n σ −2 + d 5 log 3/2 n) number of simplex pivots. We obtain our results via an improved shadow bound, key to earlier analyses as well, combined with algorithmic techniques of Borgwardt (ZOR '82) and Vershynin. As an added bonus, our analysis is completely modular, allowing us to obtain non-trivial bounds for perturbations beyond Gaussians, such as Laplace perturbations.
the Integrality Gap of Binary Integer Programs with Gaussian Data Sander Borst⋆ , Daniel Dadush⋆ , Sophie ... Huiberts, and Samarth Tiwari⋆ arXiv:2012.08346v2 [math.OC] 2 Jun 2021 Centrum Wiskunde & Informatica (CWI), Amsterdam, The Netherlands ...arXiv:2012.08346v2 fatcat:clry6bhkofg7pbnx5q6jn6fp6u
The 3-hydroxy-3-methylglutaryl coenzyme A (HMG-CoA) reductase inhibitors (statins) are widely used for the treatment of hyperlipidemia, and recent in vitro and animal data suggest that statins promote bone formation and increase bone strength. Methods: To determine whether statin use is associated with a reduced risk for fracture, we analyzed statin use and fracture rates in 4 large prospective studies (the Study of Osteoporotic Fractures, the Fracture Intervention Trial, the Heart anddoi:10.1001/archinte.164.2.146 pmid:14744837 fatcat:pnbbqjkzljetdd7s4mftg4sxqe
more »... Heart and Estrogen/Progestin Replacement Study, and the Rotterdam Study). We searched MEDLINE through January 2002 and abstracts from major scientific meetings and performed a cumulative metaanalysis of published and unpublished observational studies and clinical trials. The meta-analysis included 8 observational studies and 2 clinical trials that reported statin use and documented fracture outcomes. Results: After adjustment for multiple factors, including age, body mass index, and estrogen use, we found a (REPRINTED) ARCH INTERN MED
Explaining the excellent practical performance of the simplex method for linear programming has been a major topic of research for over 50 years. One of the most successful frameworks for understanding the simplex method was given by Spielman and Teng (JACM '04), who developed the notion of smoothed analysis. Starting from an arbitrary linear program with d variables and n constraints, Spielman and Teng analyzed the expected runtime over random perturbations of the LP (smoothed LP), wherearXiv:1711.05667v4 fatcat:6k7ww7bodbffxkhsxrrabkxz4a
more »... ed LP), where variance σ^2 Gaussian noise is added to the LP data. In particular, they gave a two-stage shadow vertex simplex algorithm which uses an expected O(d^55 n^86σ^-30) number of simplex pivots to solve the smoothed LP. Their analysis and runtime was substantially improved by Deshpande and Spielman (FOCS '05) and later Vershynin (SICOMP '09). The fastest current algorithm, due to Vershynin, solves the smoothed LP using an expected O(d^3 σ^-4log^3 n + d^9log^7 n) number of pivots, improving the dependence on n from polynomial to poly-logarithmic. While the original proof of Spielman and Teng has now been substantially simplified, the resulting analyses are still quite long and complex and the parameter dependencies far from optimal. In this work, we make substantial progress on this front, providing an improved and simpler analysis of shadow simplex methods, where our algorithm requires an expected O(d^2 √(log n)σ^-2 + d^3 log^3/2 n) number of simplex pivots. We obtain our results via an improved shadow bound, key to earlier analyses as well, combined with improvements on algorithmic techniques of Vershynin. As an added bonus, our analysis is completely modular, allowing us to obtain non-trivial bounds for perturbations beyond Gaussians, such as Laplace perturbations.
The human brain frequently generates thoughts and feelings detached from environmental demands. Investigating the rich repertoire of these mind-wandering experiences is challenging, as it depends on introspection and mapping its content requires an unknown number of dimensions. We recently developed a retrospective self-report questionnaire-the Amsterdam Resting-State Questionnaire (ARSQ)-which quantifies mind wandering along seven dimensions: "Discontinuity of Mind," "Theory of Mind," "Self,"doi:10.3389/fpsyg.2014.00271 pmid:24772097 pmcid:PMC3982068 fatcat:eiukm3676jaotkeogh6sw5yjca
more »... of Mind," "Self," "Planning," "Sleepiness," "Comfort," and "Somatic Awareness." Here, we show using confirmatory factor analysis that the ARSQ can be simplified by standardizing the number of items per factor and extending it to a 10-dimensional model, adding "Health Concern," "Visual Thought," and "Verbal Thought." We will refer to this extended ARSQ as the "ARSQ 2.0." Testing for effects of age and gender revealed no main effect for gender, yet a moderate and significant negative effect for age on the dimensions of "Self," "Planning," and "Visual Thought." Interestingly, we observed stable and significant test-retest correlations across measurement intervals of 3-32 months except for "Sleepiness" and "Health Concern." To investigate whether this stability could be related to personality traits, we correlated ARSQ scores to proxy measures of Cloninger's Temperament and Character Inventory, revealing multiple significant associations for the trait "Self-Directedness." Other traits correlated to specific ARSQ dimensions, e.g., a negative association between "Harm Avoidance" and "Comfort." Together, our results suggest that the ARSQ 2.0 is a promising instrument for quantitative studies on mind wandering and its relation to other psychological or physiological phenomena.
Following the breakthrough work of Tardos (Oper. Res. '86) in the bit-complexity model, Vavasis and Ye (Math. Prog. '96) gave the first exact algorithm for linear programming in the real model of computation with running time depending only on the constraint matrix. For solving a linear program (LP) max c ⊤ x, Ax = b, x ≥ 0, A ∈ R m×n , Vavasis and Ye developed a primal-dual interior point method using a 'layered least squares' (LLS) step, and showed that O(n 3.5 log(χ A + n)) iterationsdoi:10.1145/3357713.3384326 dblp:conf/stoc/DadushHNV20 fatcat:uu3prpzr6vddvemgnxjsbgo5sm
more »... ) iterations suffice to solve (LP) exactly, wherē χ A is a condition measure controlling the size of solutions to linear systems related to A. Monteiro and Tsuchiya (SIAM J. Optim. '03), noting that the central path is invariant under rescalings of the columns of A and c, asked whether there exists an LP algorithm depending instead on the measureχ * A , defined as the minimumχ AD value achievable by a column rescaling AD of A, and gave strong evidence that this should be the case. We resolve this open question affirmatively. Our first main contribution is an O(m 2 n 2 + n 3 ) time algorithm which works on the linear matroid of A to compute a nearly optimal diagonal rescaling D satisfyingχ AD ≤ n(χ * ) 3 . This algorithm also allows us to approximate the value ofχ A up to a factor n(χ * ) 2 . This result is in (surprising) contrast to that of Tunçel (Math. Prog. '99), who showed NP-hardness for approximatingχ A to within 2 poly(rank(A)) . The key insight for our algorithm is to work with ratios д i /д j of circuits of A-i.e., minimal linear dependencies Aд = 0-which allow us to approximate the value ofχ * A by a maximum geometric mean cycle computation in what we call the 'circuit ratio digraph' of A. While this resolves Monteiro and Tsuchiya's question by appropriate preprocessing, it falls short of providing either a truly scaling invariant algorithm or an improvement upon the base LLS analysis. In this vein, as our second main contribution we develop a scaling invariant LLS algorithm, which uses and dynamically maintains * Supported by the ERC Starting Grants ScaleOpt-757481 and QIP-805241.
doi:10.3389/fnhum.2013.00446 pmid:23964225 pmcid:PMC3737475 fatcat:6psk7zthvrcjfpxynuynsjvrx4
Supplementary Figure 1. Shisa6 structure and tissue expression. a) Schematic of the Shisa family, featuring a signal peptide (SP; blue), an extracellular domain with conserved cysteine-rich motif, a single transmembrane region (TM; green), and an intracellular domain with a type-II 1 PDZ-ligand motif (EVTV/AVTV; red). An alternative spliced exon (Ex; brown) is present in CKAMP44/Shisa9, Shisa6 and Shisa7, albeit of different size and exon number. Shisa6 and Shisa7 form a subfamily withdoi:10.1038/ncomms10682 pmid:26931375 pmcid:PMC4778035 fatcat:2dkahd4lpva2phrpk6s4g5uxuq
more »... amily with CKAMP44/Shisa9 and Shisa8. Shisa4 and Shisa5, as well as Shisa2 and Shisa3 form separate families 2 . Numbers under the protein indicate the beginning and end of the SP, TM and alternatively spliced exon domain, and the total amino acid length of the protein. The mature predicted molecular weight of each protein (including that of the alternative spliced variants) is indicated. b) Sequence alignment of the Cysteine-rich domain found in the N-terminal extracellular part of Shisa proteins, containing 8 highly conserved cysteine residues. This domain shares no proven similarity to more classical cystine-knot motifs with 6 cysteine residues found in growth factors 3,4 , toxins 5 and cyclotides 6 . c) Quantitative PCR shows that the Shisa6 gene is specifically enriched within the brain (note the log 2 -scale), and virtually absent in pancreas and testes. d) RT-PCR on cDNA generated from hippocampal RNA using primers flanking exon 3 of Shisa6. Using this RT-PCR on WT mice in duplicate, we observed a single prominent Shisa6 transcript that contains exon 3. Sequence analysis of this PCR product confirmed the presence of exon 3 (black letters) between exons 2 and 4 (gray letters). The amino acid sequence is indicated above the nucleotide sequence. Importantly, the tryptic peptide
Temporal lobe epilepsy patients are heterogeneous regarding cognitive functioning, with predominant risk of memory deficits. Despite major advances within cellular neuroscience, neuroimaging, and neuropsychology, it remains challenging to integrate memory performance with cellular characteristics and brain network topology. In a unique dataset, we investigate these cross-scale individual differences. Preoperatively, drug-resistant temporal lobe epilepsy patients (n = 31, 15 females) underwentdoi:10.1101/2021.01.31.428369 fatcat:fmqpvcjisne7lft2bi3nkno5ji
more »... emales) underwent functional magnetic resonance imaging, magnetoencephalography and/or memory testing. Macro-scale network centrality was determined, since this number of integrative functional connections a region has is crucial for memory functioning. Subsequently, non-pathological cortical tissue resected from the lateral middle temporal gyrus (default mode network) was used for single cell morphological (total dendritic length) and electrophysiological patch-clamp analysis (action potential rise speed). We expected greater macro-scale centrality to relate to longer micro-scale dendritic length and faster action potentials, and greater centrality to relate to better memory performance. Greater macro-scale centrality correlated with longer dendritic length and faster action potentials (canonical correlation coefficient = 0.329, p < 0.001). Moreover, greater macro-scale centrality was related to better memory performance (canonical correlation coefficient = 0.234, p = 0.013). We conclude that more complex neuronal morphology and faster action potential kinetics are mirrored by more integrative functional network topology of the middle temporal gyrus, which in turn is associated with better memory functioning. Thus, our cross-scale analyses reveal a significant relationship between cellular and imaging measures of network topology in the brain, which support cognitive performance in these patients.
Tonny Lagerweij and Sophie A. Dusoswa have contributed equally to this work. ...doi:10.1007/s10456-017-9565-6 pmid:28699046 pmcid:PMC5660146 fatcat:rllb7324qreffm66wb7zd3i34m
. ‡ Huibert D. Mansvelder and Christiaan P.J. de Kock share senior authorship. Abstract The size and shape of dendrites and axons are strong determinants of neuronal information processing. ...doi:10.1093/cercor/bhv188 pmid:26318661 pmcid:PMC4635923 fatcat:taicdsgoefc7pniezayji6jycq
Temporal lobe epilepsy (TLE) patients are at risk of memory deficits, which have been linked to functional network disturbances, particularly of integration of the default mode network (DMN). However, the cellular substrates of functional network integration are unknown. We leverage a unique cross-scale dataset of drug-resistant TLE patients (n = 31), who underwent pseudo resting-state functional magnetic resonance imaging (fMRI), resting-state magnetoencephalography (MEG) and/ordoi:10.1093/cercor/bhab349 pmid:34564728 fatcat:j75jtk5dcrgltb3wxrbb2eegv4
more »... d/or neuropsychological testing before neurosurgery. fMRI and MEG underwent atlas-based connectivity analyses. Functional network centrality of the lateral middle temporal gyrus, part of the DMN, was used as a measure of local network integration. Subsequently, non-pathological cortical tissue from this region was used for single cell morphological and electrophysiological patch-clamp analysis, assessing integration in terms of total dendritic length and action potential rise speed. As could be hypothesized, greater network centrality related to better memory performance. Moreover, greater network centrality correlated with more integrative properties at the cellular level across patients. We conclude that individual differences in cognitively relevant functional network integration of a DMN region are mirrored by differences in cellular integrative properties of this region in TLE patients. These findings connect previously separate scales of investigation, increasing translational insight into focal pathology and large-scale network disturbances in TLE.
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