Finding the maximum and minimum

AbstractWe consider the problem of finding the maximum out of a list of n ordered items with binary comparisons where the pth fraction of the answers may be false. It is shown that the maximum can be determined iff p < 12 and that a successful strategy needs Θ(11−p)n questions. A few similar problems are also discussed, including the problem of finding the maximum and minimum simultaneously with lies and in the nuts and bolts model

Realizability and uniqueness in graphs

AbstractConsider a finite graph G(V,E). Let us associate to G a finite list P(G) of invariants. To any P the following two natural problems arise: (R) Realizability. Given P, when is P=P(G) for some graph G?, (U) Uniqueness. Suppose P(G)=P(H) for graphs G and H. When does this imply G ≅ H? The best studied questions in this context are the degree realization problem for (R) and the reconstruction conjecture for (U). We discuss the problems (R) and (U) for the degree sequence and the size sequence of induced subgraphs for undirected and directed graphs, concentrating on the complexity of the corresponding decision problems and their connection to a natural search problem on graphs

Interlace polynomials

AbstractIn a recent paper Arratia, Bollobás and Sorkin discuss a graph polynomial defined recursively, which they call the interlace polynomial q(G,x). They present several interesting results with applications to the Alexander polynomial and state the conjecture that |q(G,−1)| is always a power of 2. In this paper we use a matrix approach to study q(G,x). We derive evaluations of q(G,x) for various x, which are difficult to obtain (if at all) by the defining recursion. Among other results we prove the conjecture for x=−1. A related interlace polynomial Q(G,x) is introduced. Finally, we show how these polynomials arise as the Martin polynomials of a certain isotropic system as introduced by Bouchet

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

Recent Advances and the Potential for Clinical Use of Autofluorescence Detection of Extra-Ophthalmic Tissues

The autofluorescence (AF) characteristics of endogenous fluorophores allow the label-free assessment and visualization of cells and tissues of the human body. While AF imaging (AFI) is well-established in ophthalmology, its clinical applications are steadily expanding to other disciplines. This review summarizes clinical advances of AF techniques published during the past decade. A systematic search of the MEDLINE database and Cochrane Library databases was performed to identify clinical AF studies in extra-ophthalmic tissues. In total, 1097 articles were identified, of which 113 from internal medicine, surgery, oral medicine, and dermatology were reviewed. While comparable technological standards exist in diabetology and cardiology, in all other disciplines, comparability between studies is limited due to the number of differing AF techniques and non-standardized imaging and data analysis. Clear evidence was found for skin AF as a surrogate for blood glucose homeostasis or cardiovascular risk grading. In thyroid surgery, foremost, less experienced surgeons may benefit from the AF-guided intraoperative separation of parathyroid from thyroid tissue. There is a growing interest in AF techniques in clinical disciplines, and promising advances have been made during the past decade. However, further research and development are mandatory to overcome the existing limitations and to maximize the clinical benefits

Strongly walk-regular graphs

We study a generalization of strongly regular graphs. We call a graph strongly walk-regular if there is an $\ell >1$ such that the number of walks of length $\ell$ from a vertex to another vertex depends only on whether the two vertices are the same, adjacent, or not adjacent. We will show that a strongly walk-regular graph must be an empty graph, a complete graph, a strongly regular graph, a disjoint union of complete bipartite graphs of the same size and isolated vertices, or a regular graph with four eigenvalues. Graphs from the first three families in this list are indeed strongly $\ell$-walk-regular for all $\ell$, whereas the graphs from the fourth family are $\ell$-walk-regular for every odd $\ell$. The case of regular graphs with four eigenvalues is the most interesting (and complicated) one. Such graphs cannot be strongly $\ell$-walk-regular for even $\ell$. We will characterize the case that regular four-eigenvalue graphs are strongly $\ell$-walk-regular for every odd $\ell$, in terms of the eigenvalues. There are several examples of infinite families of such graphs. We will show that every other regular four-eigenvalue graph can be strongly $\ell$-walk-regular for at most one $\ell$. There are several examples of infinite families of such graphs that are strongly 3-walk-regular. It however remains open whether there are any graphs that are strongly $\ell$-walk-regular for only one particular $\ell$ different from 3