Complexity of Discrete Energy Minimization Problems

Discrete energy minimization is widely-used in computer vision and machine learning for problems such as MAP inference in graphical models. The problem, in general, is notoriously intractable, and finding the global optimal solution is known to be NP-hard. However, is it possible to approximate this problem with a reasonable ratio bound on the solution quality in polynomial time? We show in this paper that the answer is no. Specifically, we show that general energy minimization, even in the 2-label pairwise case, and planar energy minimization with three or more labels are exp-APX-complete. This finding rules out the existence of any approximation algorithm with a sub-exponential approximation ratio in the input size for these two problems, including constant factor approximations. Moreover, we collect and review the computational complexity of several subclass problems and arrange them on a complexity scale consisting of three major complexity classes -- PO, APX, and exp-APX, corresponding to problems that are solvable, approximable, and inapproximable in polynomial time. Problems in the first two complexity classes can serve as alternative tractable formulations to the inapproximable ones. This paper can help vision researchers to select an appropriate model for an application or guide them in designing new algorithms.Comment: ECCV'16 accepte

No association between ACTN3 R577X and ACE I/D polymorphisms and endurance running times in 698 Caucasian athletes

Background: Studies investigating associations between ACTN3 R577X and ACE I/D genotypes and endurance athletic status have been limited by small sample sizes from mixed sport disciplines and lack quantitative measures of performance. Aim: To examine the association between ACTN3 R577X and ACE I/D genotypes and best personal running times in a large homogeneous cohort of endurance runners. Methods: We collected a total of 1064 personal best 1500, 3000, 5000 m and marathon running times of 698 male and female Caucasian endurance athletes from six countries (Australia, Greece, Italy, Poland, Russia and UK). Athletes were genotyped for ACTN3 R577X and ACE ID variants. Results: There was no association between ACTN3 R577X or ACE I/D genotype and running performance at any distance in men or women. Mean (SD) marathon times (in s) were for men: ACTN3 RR 9149 (593), RX 9221 (582), XX 9129 (582) p = 0.94; ACE DD 9182 (665), ID 9214 (549), II 9155 (492) p = 0.85; for women: ACTN3 RR 10796 (818), RX 10667 (695), XX 10675 (553) p = 0.36; ACE DD 10604 (561), ID 10766 (740), II 10771 (708) p = 0.21. Furthermore, there were no associations between these variants and running time for any distance in a sub-analysis of athletes with personal records within 20% of world records. Conclusions: Thus, consistent with most case-control studies, this multi-cohort quantitative analysis demonstrates it is unlikely that ACTN3 XX genotype provides an advantage in competitive endurance running performance. For ACE II genotype, some prior studies show an association but others do not. Our data indicate it is also unlikely that ACE II genotype provides an advantage in endurance running

Search for a Technicolor omega_T Particle in Events with a Photon and a b-quark Jet at CDF

If the Technicolor omega_T particle exists, a likely decay mode is omega_T -> gamma pi_T, followed by pi_T -> bb-bar, yielding the signature gamma bb-bar. We have searched 85 pb^-1 of data collected by the CDF experiment at the Fermilab Tevatron for events with a photon and two jets, where one of the jets must contain a secondary vertex implying the presence of a b quark. We find no excess of events above standard model expectations. We express the result of an exclusion region in the M_omega_T - M_pi_T mass plane.Comment: 14 pages, 2 figures. Available from the CDF server (PS with figs): http://www-cdf.fnal.gov/physics/pub98/cdf4674_omega_t_prl_4.ps FERMILAB-PUB-98/321-

Measurement of the B0 anti-B0 oscillation frequency using l- D*+ pairs and lepton flavor tags

The oscillation frequency Delta-md of B0 anti-B0 mixing is measured using the partially reconstructed semileptonic decay anti-B0 -> l- nubar D*+ X. The data sample was collected with the CDF detector at the Fermilab Tevatron collider during 1992 - 1995 by triggering on the existence of two lepton candidates in an event, and corresponds to about 110 pb-1 of pbar p collisions at sqrt(s) = 1.8 TeV. We estimate the proper decay time of the anti-B0 meson from the measured decay length and reconstructed momentum of the l- D*+ system. The charge of the lepton in the final state identifies the flavor of the anti-B0 meson at its decay. The second lepton in the event is used to infer the flavor of the anti-B0 meson at production. We measure the oscillation frequency to be Delta-md = 0.516 +/- 0.099 +0.029 -0.035 ps-1, where the first uncertainty is statistical and the second is systematic.Comment: 30 pages, 7 figures. Submitted to Physical Review

Search for New Particles Decaying to top-antitop in proton-antiproton collisions at squareroot(s)=1.8 TeV

We use 106 \ipb of data collected with the Collider Detector at Fermilab to search for narrow-width, vector particles decaying to a top and an anti-top quark. Model independent upper limits on the cross section for narrow, vector resonances decaying to \ttbar are presented. At the 95% confidence level, we exclude the existence of a leptophobic \zpr boson in a model of topcolor-assisted technicolor with mass M_{\zpr} $<$ 480 \gev for natural width $\Gamma$ = 0.012 M_{\zpr}, and M_{\zpr} $<$ 780 \gev for $\Gamma$ = 0.04 M_{\zpr}.Comment: The CDF Collaboration, submitted to PRL 25-Feb-200

Double Diffraction Dissociation at the Fermilab Tevatron Collider

We present results from a measurement of double diffraction dissociation in $\bar pp$ collisions at the Fermilab Tevatron collider. The production cross section for events with a central pseudorapidity gap of width $\Delta\eta^0>3$ (overlapping $\eta=0$) is found to be $4.43\pm 0.02{(stat)}{\pm 1.18}{(syst) mb}$ [$3.42\pm 0.01{(stat)}{\pm 1.09}{(syst) mb}$] at $\sqrt{s}=1800$ [630] GeV. Our results are compared with previous measurements and with predictions based on Regge theory and factorization.Comment: 10 pages, 4 figures, using RevTeX. Submitted to Physical Review Letter

A Measurement of the Differential Dijet Mass Cross Section in p-pbar Collisions at sqrt{s}=1.8 TeV

We present a measurement of the cross section for production of two or more jets as a function of dijet mass, based on an integrated luminosity of 86 pb^-1 collected with the Collider Detector at Fermilab. Our dijet mass spectrum is described within errors by next-to-leading order QCD predictions using CTEQ4HJ parton distributions, and is in good agreement with a similar measurement from the D0 experiment.Comment: 18 pages including 2 figures and 3 tables. Submitted to Phys. Rev. D Rapid Communication

Search for Gluinos and Scalar Quarks in ppˉp\bar{p} Collisions at s=1.8\sqrt{s}=1.8 TeV using the Missing Energy plus Multijets Signature

We have performed a search for gluinos (\gls) and squarks (\sq) in a data sample of 84 pb$^{-1}$ of \ppb collisions at $\sqrt{s}$ = 1.8 TeV, recorded by the Collider Detector at Fermilab, by investigating the final state of large missing transverse energy and 3 or more jets, a characteristic signature in R-parity-conserving supersymmetric models. The analysis has been performed `blind', in that the inspection of the signal region is made only after the predictions from Standard Model backgrounds have been calculated. Comparing the data with predictions of constrained supersymmetric models, we exclude gluino masses below 195 \gev (95% C.L.), independent of the squark mass. For the case \msq \approx \mgls, gluino masses below 300 \gev are excluded.Comment: 7 pages, 3 figure

Diffractive Dijet Production at sqrt(s)=630 and 1800 GeV at the Fermilab Tevatron

We report a measurement of the diffractive structure function $F_{jj}^D$ of the antiproton obtained from a study of dijet events produced in association with a leading antiproton in $\bar pp$ collisions at $\sqrt s=630$ GeV at the Fermilab Tevatron. The ratio of $F_{jj}^D$ at $\sqrt s=630$ GeV to $F_{jj}^D$ obtained from a similar measurement at $\sqrt s=1800$ GeV is compared with expectations from QCD factorization and with theoretical predictions. We also report a measurement of the $\xi$ ($x$-Pomeron) and $\beta$ ($x$ of parton in Pomeron) dependence of $F_{jj}^D$ at $\sqrt s=1800$ GeV. In the region $0.035<\xi<0.095$, $|t|<1$ GeV$^2$ and $\beta<0.5$, $F_{jj}^D(\beta,\xi)$ is found to be of the form $\beta^{-1.0\pm 0.1} \xi^{-0.9\pm 0.1}$, which obeys $\beta$-$\xi$ factorization.Comment: LaTeX, 9 pages, Submitted to Phys. Rev. Letter