Quasipolynomial size frege proofs of Frankl's Theorem on the trace of sets

We extend results of Bonet, Buss and Pitassi on Bondy's Theorem and of Nozaki, Arai and Arai on Bollobas' Theorem by proving that Frankl's Theorem on the trace of sets has quasipolynomial size Frege proofs. For constant values of the parameter t, we prove that Frankl's Theorem has polynomial size AC(0)-Frege proofs from instances of the pigeonhole principle.Peer ReviewedPostprint (author's final draft

Quantum anomalies and linear response theory

The analysis of diffusive energy spreading in quantized chaotic driven systems, leads to a universal paradigm for the emergence of a quantum anomaly. In the classical approximation a driven chaotic system exhibits stochastic-like diffusion in energy space with a coefficient $D$ that is proportional to the intensity $\epsilon^2$ of the driving. In the corresponding quantized problem the coherent transitions are characterized by a generalized Wigner time $t_{\epsilon}$, and a self-generated (intrinsic) dephasing process leads to non-linear dependence of $D$ on $\epsilon^2$.Comment: 8 pages, 2 figures, textual improvements (as in published version

2-D Tucker is PPA complete

The 2-D Tucker search problem is shown to be PPA-hard under many-one reductions; therefore it is complete for PPA. The same holds for k-D Tucker for all k≥2. This corrects a claim in the literature that the Tucker search problem is in PPAD.Peer ReviewedPostprint (author's final draft

Anomalous decay of a prepared state due to non-Ohmic coupling to the continuum

We study the decay of a prepared state $E_0$ into a continuum {E_k} in the case of non-Ohmic models. This means that the coupling is $|V_{k,0}| \propto |E_k-E_0|^{s-1}$ with $s \ne 1$. We find that irrespective of model details there is a universal generalized Wigner time $t_0$ that characterizes the evolution of the survival probability $P_0(t)$. The generic decay behavior which is implied by rate equation phenomenology is a slowing down stretched exponential, reflecting the gradual resolution of the bandprofile. But depending on non-universal features of the model a power-law decay might take over: it is only for an Ohmic coupling to the continuum that we get a robust exponential decay that is insensitive to the nature of the intra-continuum couplings. The analysis highlights the co-existence of perturbative and non-perturbative features in the dynamics. It turns out that there are special circumstances in which $t_0$ is reflected in the spreading process and not only in the survival probability, contrary to the naive linear response theory expectation.Comment: 13 pages, 11 figure

Short proofs of the Kneser-Lovász coloring principle

We prove that propositional translations of the Kneser–Lovász theorem have polynomial size extended Frege proofs and quasi-polynomial size Frege proofs for all fixed values of k. We present a new counting-based combinatorial proof of the K neser–Lovász theorem based on the Hilton–Milner theorem; this avoids the topological arguments of prior proofs for all but finitely many base cases. We introduce new “truncated Tucker lemma” principles, which are miniaturizations of the octahedral Tucker lemma. The truncated Tucker lemma implies the Kneser–Lovász theorem. We show that the k=1 case of the truncated Tucker lemma has polynomial size extended Frege proofs.Peer ReviewedPostprint (author's final draft

Quantum decay into a non-flat continuum

We study the decay of a prepared state into non-flat continuum. We find that the survival probability $P(t)$ might exhibit either stretched-exponential or power-law decay, depending on non-universal features of the model. Still there is a universal characteristic time $t_0$ that does not depend on the functional form. It is only for a flat continuum that we get a robust exponential decay that is insensitive to the nature of the intra-continuum couplings. The analysis highlights the co-existence of perturbative and non-perturbative features in the local density of states, and the non-linear dependence of $1/t_0$ on the strength of the coupling.Comment: 10 pages, 4 figure

Accuracy of Capsule Colonoscopy in Detecting Colorectal Polyps in a Screening Population

BACKGROUND & AIMS: Capsule colonoscopy is a minimally invasive imaging method. We measured the accuracy of this technology in detecting polyps 6 mm or larger in an average-risk screening population. METHODS: In a prospective study, asymptomatic subjects (n = 884) underwent capsule colonoscopy followed by conventional colonoscopy (the reference) several weeks later, with an endoscopist blinded to capsule results, at 10 centers in the United States and 6 centers in Israel from June 2011 through April 2012. An unblinded colonoscopy was performed on subjects found to have lesions 6 mm or larger by capsule but not conventional colonoscopy. RESULTS: Among the 884 subjects enrolled, 695 (79%) were included in the analysis of capsule performance for all polyps. There were 77 exclusions (9%) for inadequate cleansing and whole-colon capsule transit time fewer than 40 minutes, 45 exclusions (5%) before capsule ingestion, 15 exclusions (2%) after ingestion and before colonoscopy, and 15 exclusions (2%) for site termination. Capsule colonoscopy identified subjects with 1 or more polyps 6 mm or larger with 81% sensitivity (95% confidence interval [CI], 77%-84%) and 93% specificity (95% CI, 91%-95%), and polyps 10 mm or larger with 80% sensitivity (95% CI, 74%-86%) and 97% specificity (95% CI, 96%-98%). Capsule colonoscopy identified subjects with 1 or more conventional adenomas 6 mm or larger with 88% sensitivity (95% CI, 82%-93) and 82% specificity (95% CI, 80%-83%), and 10 mm or larger with 92% sensitivity (95% CI, 82%-97%) and 95% specificity (95% CI, 94%-95%). Sessile serrated polyps and hyperplastic polyps accounted for 26% and 37%, respectively, of false-negative findings from capsule analyses. CONCLUSIONS: In an average-risk screening population, technically adequate capsule colonoscopy identified individuals with 1 or more conventional adenomas 6 mm or larger with 88% sensitivity and 82% specificity. Capsule performance seems adequate for patients who cannot undergo colonoscopy or who had incomplete colonoscopies. Additional studies are needed to improve capsule detection of serrated lesions. Clinicaltrials.gov number: NCT01372878

The proof and search complexity of three combinatorial principles

This work concerns the propositional proof complexity and computational complexity of Frankl's theorem on the trace of sets, the Kneser-Lovász theorem, and the Tucker lemma.We show that propositional translations of Frankl's theorem on the trace of sets has quasi-polynomial size Frege proofs. For constant values of the parameter t, we prove that Frankl's theorem has polynomial size AC0-Frege proofs from instances of the pigeonhole principle.We prove that propositional translations of the Kneser-Lovász theorem have polynomial size extended Frege proofs and quasi-polynomial size Frege proofs for all fixed values of k. We present a new counting-based combinatorial proof of the Kneser-Lovász theorem that avoids the topological arguments of prior proofs for all but finitely many base cases. We introduce new ``truncated Tucker lemma'' principles, which are miniaturizations of the octahedral Tucker lemma. The truncated Tucker lemma implies the Kneser-Lovász theorem. We show that the k=1 case of the truncated Tucker lemma has polynomial size extended Frege proofs.We show that the 2-D TUCKER search problem is PPA-hard under many-one reductions; therefore it is complete for PPA. The same holds for k-D Tucker for all k >= 2. This corrects a claim in the literature that the Tucker search problem is in PPAD.Frankl's theorem, the Kneser-Lovász theorem, and the truncated Tucker lemma are all shown to give total NP search problems. These problems are all shown to be PPP-hard under many-one reductions