Quasirandomness in hypergraphs

An $n$-vertex graph $G$ of edge density $p$ is considered to be quasirandom if it shares several important properties with the random graph $G(n,p)$. A well-known theorem of Chung, Graham and Wilson states that many such `typical' properties are asymptotically equivalent and, thus, a graph $G$ possessing one such property automatically satisfies the others. In recent years, work in this area has focused on uncovering more quasirandom graph properties and on extending the known results to other discrete structures. In the context of hypergraphs, however, one may consider several different notions of quasirandomness. A complete description of these notions has been provided recently by Towsner, who proved several central equivalences using an analytic framework. We give short and purely combinatorial proofs of the main equivalences in Towsner's result.Comment: 19 page

The Relationship between Personality Organization and Psychiatric Classification in Chronic Pain Patients

The assessment of PO is a crucial issue for diagnosis and treatment planning in CPPs, since it represents a measure of structural impairment that is to a considerable extent independent of axis I and II diagnoses. Moreover, the STIPO dimensional rating focuses on the most salient dysfunctions at a given time. Copyright (C) 2010 S. Karger AG, BaselBackground: The present study investigated the relationship between psychiatric classification and personality organization (PO) in a secondary/tertiary clinical sample of chronic pain patients (CPPs). Sampling and Methods: Forty-three patients were administered the Structured Clinical Interview for DSM-IV (SCID I+II) and the Structured Interview of Personality Organization (STIPO). The prevalence of axis I and axis II disorders was correlated with the STIPO level of PO. The STIPO dimensional ratings of patients without personality disorder (PD) were compared to those of patients diagnosed with one or more PDs. Results: Axis I comorbidity was high (93%), and 63% of the patients met the criteria for at least one axis II diagnosis. Twenty-five patients (58%) were diagnosed as borderline PO, with high-level impairments in the dimensions `coping/rigidity', `primitive defenses' and `identity'. Higher axis I and axis II comorbidity corresponded with greater severity of PO impairment. No difference was found between the dimensional ratings of patients without PD and those of patients with one or more PDs. Conclusions

Minimum and maximum against k lies

A neat 1972 result of Pohl asserts that [3n/2]-2 comparisons are sufficient, and also necessary in the worst case, for finding both the minimum and the maximum of an n-element totally ordered set. The set is accessed via an oracle for pairwise comparisons. More recently, the problem has been studied in the context of the Renyi-Ulam liar games, where the oracle may give up to k false answers. For large k, an upper bound due to Aigner shows that (k+O(\sqrt{k}))n comparisons suffice. We improve on this by providing an algorithm with at most (k+1+C)n+O(k^3) comparisons for some constant C. The known lower bounds are of the form (k+1+c_k)n-D, for some constant D, where c_0=0.5, c_1=23/32=0.71875, and c_k=\Omega(2^{-5k/4}) as k goes to infinity.Comment: 11 pages, 3 figure

Using Citizen Scientists to Evaluate Light Traps for Catching Brown Marmorated Stink Bugs in Homes in Virginia

More and more, citizen scientists are playing an integral role in research studies. This has been particularly evident as entomologists unravel the biology, spread, and management of the brown marmorated stink bug, which has plagued many homeowners in the mid-Atlantic U.S. in recent years. We used citizen scientists to evaluate different indoor light traps for catching the bugs in houses. Throughout the late winter and early spring months, these traps were tested inside homes and enabled us to determine that the most efficacious trap was an aluminum foil water pan trap, developed by—you guessed it—a citizen scientist

Imaging geometry through dynamics: the observable representation

For many stochastic processes there is an underlying coordinate space, $V$, with the process moving from point to point in $V$ or on variables (such as spin configurations) defined with respect to $V$. There is a matrix of transition probabilities (whether between points in $V$ or between variables defined on $V$) and we focus on its ``slow'' eigenvectors, those with eigenvalues closest to that of the stationary eigenvector. These eigenvectors are the ``observables,'' and they can be used to recover geometrical features of $V$

The Cop Number of the One-Cop-Moves Game on Planar Graphs

Cops and robbers is a vertex-pursuit game played on graphs. In the classical cops-and-robbers game, a set of cops and a robber occupy the vertices of the graph and move alternately along the graph's edges with perfect information about each other's positions. If a cop eventually occupies the same vertex as the robber, then the cops win; the robber wins if she can indefinitely evade capture. Aigner and Frommer established that in every connected planar graph, three cops are sufficient to capture a single robber. In this paper, we consider a recently studied variant of the cops-and-robbers game, alternately called the one-active-cop game, one-cop-moves game or the lazy-cops-and-robbers game, where at most one cop can move during any round. We show that Aigner and Frommer's result does not generalise to this game variant by constructing a connected planar graph on which a robber can indefinitely evade three cops in the one-cop-moves game. This answers a question recently raised by Sullivan, Townsend and Werzanski.Comment: 32 page

Small rainbow cliques in randomly perturbed dense graphs

For two graphs G and H, write G rbw −→ H if G has the property that every proper colouring of its edges yields a rainbow copy of H. We study the thresholds for such so-called anti-Ramsey properties in randomly perturbed dense graphs, which are unions of the form G ∪ G(n, p), where G is an n-vertex graph with edge-density at least d > 0, and d is independent of n. In a companion paper, we proved that the threshold for the property G ∪ G(n, p) rbw −→ K` is n −1/m2(Kd`/2e) , whenever ` ≥ 9. For smaller `, the thresholds behave more erratically, and for 4 ≤ ` ≤ 7 they deviate downwards significantly from the aforementioned aesthetic form capturing the thresholds for large cliques. In particular, we show that the thresholds for ` ∈ {4, 5, 7} are n −5/4 , n −1 , and n −7/15, respectively. For ` ∈ {6, 8} we determine the threshold up to a (1 + o(1))-factor in the exponent: they are n −(2/3+o(1)) and n −(2/5+o(1)), respectively. For ` = 3, the threshold is n −2 ; this follows from a more general result about odd cycles in our companion paper

Long-Range Order in Electronic Transport through Disordered Metal Films

Ultracold atom magnetic field microscopy enables the probing of current flow patterns in planar structures with unprecedented sensitivity. In polycrystalline metal (gold) films we observe long-range correlations forming organized patterns oriented at +/- 45 deg relative to the mean current flow, even at room temperature and at length scales orders of magnitude larger than the diffusion length or the grain size. The preference to form patterns at these angles is a direct consequence of universal scattering properties at defects. The observed amplitude of the current direction fluctuations scales inversely to that expected from the relative thickness variations, the grain size and the defect concentration, all determined independently by standard methods. This indicates that ultracold atom magnetometry enables new insight into the interplay between disorder and transport

Uniform generation in trace monoids

We consider the problem of random uniform generation of traces (the elements of a free partially commutative monoid) in light of the uniform measure on the boundary at infinity of the associated monoid. We obtain a product decomposition of the uniform measure at infinity if the trace monoid has several irreducible components-a case where other notions such as Parry measures, are not defined. Random generation algorithms are then examined.Comment: Full version of the paper in MFCS 2015 with the same titl

Die Spontanheilungsversuche des vorderen Kreuzbands : eine experimentelle Untersuchung

Fragestellung Spontanheilungen von Rupturen des vorderen Kreuzbandes (VKB) wurden wiederholt mittels MRT beschrieben. In grundlegenden tierexperimentellen Untersuchungen wird geschlussfolgert, dass es keine Regeneration gäbe. Die Morphologie der Spontanheilung des VKB wurde im Tiermodell des Kaninchens untersucht. Methoden 32 männliche Kaninchen wurden medial arthrotomiert und das VKB durchtrennt. Die Durchtrennung erfolgte unter Sicht mittels Nr. 15 Skalpell, zusätzlich wurde die vollständige Trennung der Stümpfe durch mehrfache Instrumentenpassage kontrolliert. Eine Resektion von Fasern erfolgte nicht. Je 8 Tiere wurden 2, 4, 8 und 12 Wochen nach dem Eingriff getötet. Die Morphologie der Heilungsverläufe wurde nach Lo et al. [1] klassifiziert, neue Typen der Klassifikation hinzugefügt. Typ B (intrasynoviale Ruptur) und Typ C (knöcherner Ausriss) waren studienbedingt nicht möglich. Die Studie war vom Regierungspräsidium genehmigt. Ergebnisse Die untersuchten Tiere hatten einen unauffälligen postoperativen Verlauf. Bei unterschiedlicher Ausprägung hatten alle Tiere makroskopisch eine Knorpelschädigung. Nach chirurgischer Durchtrennung waren die VKBenden durchschnitten (mop ended Typ A). Dieser Typ wurde bei der Dissektion nicht mehr vorgefunden. Die VKBstümpfe waren bei Dissektion: retrahiert (Typ D), mit dem hinteren Kreuzband verwachsen (E), resorbiert (F), miteinander verbunden = narbengeheilt (G), oder es lag eine Kombination (H) verschiedener Typen vor. Als neue Typen wurden Verwachsungen mit dem Meniskus (I) oder mit der Gelenkkapsel bzw. dem Fettkörper (K) beschrieben. Die VKBstümpfe waren gering (G 1 = 7), deutlich (G2 = 3 bzw. 4 insges. bei zusätzlicher Verwachsung mit dem Innenmeniskus) oder hypertroph (G 3 = 3) miteinander verwachsen. [Tab. 1] Schlussfolgerungen Der VKBriss führt häufig zur Kniegelenksinstabilität und Osteoarthrose. Nach Durchtrennung des VKB wird in Studien der Osteoarthroseforschung im Kaninchenmodell der Befund nie detailliert. In einem systematischen Vergleich der Regenerationsfähigkeit von partiell und komplett durchtrennten VKBs fanden Hefti et al. [2] weder bei skeletall unreifen noch bei jungen erwachsenen Kaninchen eine Regeneration nach kompletter Durchtrennung. Sie berichteten als Regelfall die Resorption nach 3 Monaten, in 2 Fällen Verwachsungen mit dem hinteren Kreuzband. Die hier berichteten Daten sind im Gegensatz zu Hefti's Untersuchungen. Sie stimmen aber gut mit humanen MRT-Untersuchungen und Arthroskopien nach Kreuzbandverletzungen überein. Das VKB versucht durch Verwachsung eine Heilung der VKBstümpfe zu erzielen oder Anschluss an andere Kniegelenksstrukturen zu gewinnen. Somit besteht auch im Tiermodell des Kaninchens eine gewisse Spontanheilungsaktivität des VKB, deren biomechanische Stabilität allerdings oft unzureichend erschien. Eine Kniegelenksarthrose entwickelte sich in den untersuchten Gelenken