Combining Contrast Invariant L1 Data Fidelities with Nonlinear Spectral Image Decomposition

This paper focuses on multi-scale approaches for variational methods and corresponding gradient flows. Recently, for convex regularization functionals such as total variation, new theory and algorithms for nonlinear eigenvalue problems via nonlinear spectral decompositions have been developed. Those methods open new directions for advanced image filtering. However, for an effective use in image segmentation and shape decomposition, a clear interpretation of the spectral response regarding size and intensity scales is needed but lacking in current approaches. In this context, $L^1$ data fidelities are particularly helpful due to their interesting multi-scale properties such as contrast invariance. Hence, the novelty of this work is the combination of $L^1$-based multi-scale methods with nonlinear spectral decompositions. We compare $L^1$ with $L^2$ scale-space methods in view of spectral image representation and decomposition. We show that the contrast invariant multi-scale behavior of $L^1-TV$ promotes sparsity in the spectral response providing more informative decompositions. We provide a numerical method and analyze synthetic and biomedical images at which decomposition leads to improved segmentation.Comment: 13 pages, 7 figures, conference SSVM 201

Tacrolimus in pediatric renal transplantation

Tacrolimus was used as the primary immunosuppressive agent in 69 pediatric renal transplantations between December 17, 1989, and June 30, 1995. Children undergoing concomitant or prior liver and/or intestinal transplantation were excluded from analysis. The mean recipient age was 10.3±5.0 years (range, 0.7-17.5 years). Seventeen (24.6%) children were undergoing retransplantation, and six (8.7%) had a panel reactive antibody level of 40% or higher. Thirty-nine (57%) cases were with cadaveric kidneys, and 30 (43%) were with living donors. The mean donor age was 28.0±14.7 years (range, 1.0-50.0 years), and the mean cold ischemia time for the cadaveric kidneys was 27.0±9.4 hr. The antigen match was 2.7±1.2, and the mismatch was 3.1±1.2. All patients received tacrolimus and steroids, without antibody induction, and 26% received azathioprine as well. The mean follow-up was 32±20 months. One- and 4-year actuarial patient survival rates were 100% and 95%. One- and 4-year actuarial graft survival rates were 99% and 85%. The mean serum creatinine level was 1.2±0.8 mg/dl, and the calculated creatinine clearance was 82±26 ml/min/1.73 m2. The mean tacrolimus dose was 0.22±0.14 mg/kg/day, and the level was 9.5±4.8 ng/ml. The mean prednisone dose was 2.1±4.9 mg/day (0.07±0.17 mg/kg/day), and 73% of successfully transplanted children were off prednisone. Seventy-nine percent were not taking any antihypertensive medications. The mean serum cholesterol level was 158±54 mg/dl. The incidence of delayed graft function was 4.3%. The incidence of rejection was 49%, and the incidence of steroid-resistant rejection was 6%. The incidence of rejection decreased to 27% in the most recent 26 cases (January 1994 through June 1995). The incidence of new-onset diabetes was 10.1%; six of the seven affected children were able to be weaned off insulin. The incidence of cytomegalovirus disease was 13%, and that of posttransplant lymphoproliferative disorder was 10%; the incidence of posttransplant lymphoproliferative disorder in the last 40 transplants was 5% (two cases). All of the children who developed posttransplant lymphoproliferative disorder are alive and have functioning allografts. Based on this data, we believe that tacrolimus is a superior immunosuppressive agent in pediatric renal transplant patients, with excellent short- and medium-term patient and graft survival, an ability to withdraw steroids in the majority of patients, and, with more experience, a decreasing rate of rejection and vital complications

FK506 IN PEDIATRIC KIDNEY-TRANSPLANTATION - PRIMARY AND RESCUE EXPERIENCE

Between December 14, 1989, and December 17, 1993,43 patients undergoing kidney transplantation alone at the Children’s Hospital of Pittsburgh received FK506 as the primary immunosuppressive agent. The mean recipient age was 10.2 ± 4.8 years (range 0.7–17.4), with 7 (16%) children under 5 years of age and 2 (5%) under 2 years of age. Fifteen (35%) children underwent retransplantation, and 5 (12%) had a panel reactive antibody level greater than 40%. Twenty-two (51%) cases were with cadaveric donors, and 21 (49%) were with living donors. The mean follow-up is 25 ± 14 months. There were no deaths. One and three year actuarial graft survival was 98% and 85%. The mean serum creatinine and BUN were 1.2 ± 0.6 mg/dl and 26 ± 11 mg/dl; the calculated creatinine clearance was 75 ± 23 ml/min/1.73 m(2). Twenty-four (62%) patients have been successfully withdrawn from steroids, and 24 (62%) require no anti-hypertensive medication. Improved growth was seen, particularly in pre-adolescent children off steroids. Between July 28, 1990, and December 2, 1993, 24 children were referred for rescue therapy with FK506, 14.6 ± 16.4 months (range 1.1–53.2) after transplantation. Nineteen (79%) were referred because of resistant rejection; 4 (17%) were referred because of proteinuria; 1 (4%) was switched because of steroid-related obesity. There were no deaths. One and two year graft survival was 75% and 68%. Seventeen (71%) patients were successfully rescued, including 1 of 2 patients who arrived on dialysis. Four (24%) of the successfully rescued patients were weaned off steroids. While not without side effects, which include nephrotoxicity, neurotoxicity, diabetogenicity, and viral complications, FK506 appears to be an effective immunosuppressive agent for both primary and rescue therapy after kidney transplantation. Its steroid-sparing qualities may be of particular importance in the pediatric population

Utilitarian Collective Choice and Voting

In his seminal Social Choice and Individual Values, Kenneth Arrow stated that his theory applies to voting. Many voting theorists have been convinced that, on account of Arrow’s theorem, all voting methods must be seriously flawed. Arrow’s theory is strictly ordinal, the cardinal aggregation of preferences being explicitly rejected. In this paper I point out that all voting methods are cardinal and therefore outside the reach of Arrow’s result. Parallel to Arrow’s ordinal approach, there evolved a consistent cardinal theory of collective choice. This theory, most prominently associated with the work of Harsanyi, continued the older utilitarian tradition in a more formal style. The purpose of this paper is to show that various derivations of utilitarian SWFs can also be used to derive utilitarian voting (UV). By this I mean a voting rule that allows the voter to score each alternative in accordance with a given scale. UV-k indicates a scale with k distinct values. The general theory leaves k to be determined on pragmatic grounds. A (1,0) scale gives approval voting. I prefer the scale (1,0,-1) and refer to the resulting voting rule as evaluative voting. A conclusion of the paper is that the defects of conventional voting methods result not from Arrow’s theorem, but rather from restrictions imposed on voters’ expression of their preferences. The analysis is extended to strategic voting, utilizing a novel set of assumptions regarding voter behavior

Searching for network modules

When analyzing complex networks a key target is to uncover their modular structure, which means searching for a family of modules, namely node subsets spanning each a subnetwork more densely connected than the average. This work proposes a novel type of objective function for graph clustering, in the form of a multilinear polynomial whose coefficients are determined by network topology. It may be thought of as a potential function, to be maximized, taking its values on fuzzy clusterings or families of fuzzy subsets of nodes over which every node distributes a unit membership. When suitably parametrized, this potential is shown to attain its maximum when every node concentrates its all unit membership on some module. The output thus is a partition, while the original discrete optimization problem is turned into a continuous version allowing to conceive alternative search strategies. The instance of the problem being a pseudo-Boolean function assigning real-valued cluster scores to node subsets, modularity maximization is employed to exemplify a so-called quadratic form, in that the scores of singletons and pairs also fully determine the scores of larger clusters, while the resulting multilinear polynomial potential function has degree 2. After considering further quadratic instances, different from modularity and obtained by interpreting network topology in alternative manners, a greedy local-search strategy for the continuous framework is analytically compared with an existing greedy agglomerative procedure for the discrete case. Overlapping is finally discussed in terms of multiple runs, i.e. several local searches with different initializations.Comment: 10 page

Strong laws of large numbers for sub-linear expectations

We investigate three kinds of strong laws of large numbers for capacities with a new notion of independently and identically distributed (IID) random variables for sub-linear expectations initiated by Peng. It turns out that these theorems are natural and fairly neat extensions of the classical Kolmogorov's strong law of large numbers to the case where probability measures are no longer additive. An important feature of these strong laws of large numbers is to provide a frequentist perspective on capacities.Comment: 10 page

Propulsion in a viscoelastic fluid

Flagella beating in complex fluids are significantly influenced by viscoelastic stresses. Relevant examples include the ciliary transport of respiratory airway mucus and the motion of spermatozoa in the mucus-filled female reproductive tract. We consider the simplest model of such propulsion and transport in a complex fluid, a waving sheet of small amplitude free to move in a polymeric fluid with a single relaxation time. We show that, compared to self-propulsion in a Newtonian fluid occurring at a velocity U_N, the sheet swims (or transports fluid) with velocity U / U_N = [1+De^2 (eta_s)/(eta) ]/[1+De^2], where eta_s is the viscosity of the Newtonian solvent, eta is the zero-shear-rate viscosity of the polymeric fluid, and De is the Deborah number for the wave motion, product of the wave frequency by the fluid relaxation time. Similar expressions are derived for the rate of work of the sheet and the mechanical efficiency of the motion. These results are shown to be independent of the particular nonlinear constitutive equations chosen for the fluid, and are valid for both waves of tangential and normal motion. The generalization to more than one relaxation time is also provided. In stark contrast with the Newtonian case, these calculations suggest that transport and locomotion in a non-Newtonian fluid can be conveniently tuned without having to modify the waving gait of the sheet but instead by passively modulating the material properties of the liquid.Comment: 21 pages, 1 figur

Apparent non-canonical trans-splicing is generated by reverse transcriptase in vitro

Trans-splicing, the in vivo joining of two RNA molecules, is well characterized in several groups of simple organisms but was long thought absent from fungi, plants and mammals. However, recent bioinformatic analyses of expressed sequence tag (EST) databases suggested widespread trans-splicing in mammals^1-2^. Splicing, including the characterised trans-splicing systems, involves conserved sequences at the splice junctions. Our analysis of a yeast non-coding RNA revealed that around 30% of the products of reverse transcription lacked an internal region of 117 nt, suggesting that the RNA was spliced. The junction sequences lacked canonical splice-sites but were flanked by direct repeats, and further analyses indicated that the apparent splicing actually arose because reverse transcriptase can switch templates during transcription^3^. Many newly identified, apparently trans-spliced, RNAs lacked canonical splice sites but were flanked by short regions of homology, leading us to question their authenticity. Here we report that all reported categories of non-canonical splicing could be replicated using an in vitro reverse transcription system with highly purified RNA substrates. We observed the reproducible occurrence of ostensible trans-splicing, exon shuffling and sense-antisense fusions. The latter generate apparent antisense non-coding RNAs, which are also reported to be abundant in humans^4^. Different reverse transcriptases can generate different products of template switching, providing a simple diagnostic. Many reported examples of splicing in the absence of canonical splicing signals may be artefacts of cDNA preparation

Grey and white matter correlates of recent and remote autobiographical memory retrieval:Insights from the dementias

The capacity to remember self-referential past events relies on the integrity of a distributed neural network. Controversy exists, however, regarding the involvement of specific brain structures for the retrieval of recently experienced versus more distant events. Here, we explored how characteristic patterns of atrophy in neurodegenerative disorders differentially disrupt remote versus recent autobiographical memory. Eleven behavioural-variant frontotemporal dementia, 10 semantic dementia, 15 Alzheimer's disease patients and 14 healthy older Controls completed the Autobiographical Interview. All patient groups displayed significant remote memory impairments relative to Controls. Similarly, recent period retrieval was significantly compromised in behavioural-variant frontotemporal dementia and Alzheimer's disease, yet semantic dementia patients scored in line with Controls. Voxel-based morphometry and diffusion tensor imaging analyses, for all participants combined, were conducted to investigate grey and white matter correlates of remote and recent autobiographical memory retrieval. Neural correlates common to both recent and remote time periods were identified, including the hippocampus, medial prefrontal, and frontopolar cortices, and the forceps minor and left hippocampal portion of the cingulum bundle. Regions exclusively implicated in each time period were also identified. The integrity of the anterior temporal cortices was related to the retrieval of remote memories, whereas the posterior cingulate cortex emerged as a structure significantly associated with recent autobiographical memory retrieval. This study represents the first investigation of the grey and white matter correlates of remote and recent autobiographical memory retrieval in neurodegenerative disorders. Our findings demonstrate the importance of core brain structures, including the medial prefrontal cortex and hippocampus, irrespective of time period, and point towards the contribution of discrete regions in mediating successful retrieval of distant versus recently experienced events

Positive approximations of the inverse of fractional powers of SPD M-matrices

This study is motivated by the recent development in the fractional calculus and its applications. During last few years, several different techniques are proposed to localize the nonlocal fractional diffusion operator. They are based on transformation of the original problem to a local elliptic or pseudoparabolic problem, or to an integral representation of the solution, thus increasing the dimension of the computational domain. More recently, an alternative approach aimed at reducing the computational complexity was developed. The linear algebraic system $\cal A^\alpha \bf u=\bf f$, $0< \alpha <1$ is considered, where $\cal A$ is a properly normalized (scalded) symmetric and positive definite matrix obtained from finite element or finite difference approximation of second order elliptic problems in $\Omega\subset\mathbb{R}^d$, $d=1,2,3$. The method is based on best uniform rational approximations (BURA) of the function $t^{\beta-\alpha}$ for $0 < t \le 1$ and natural $\beta$. The maximum principles are among the major qualitative properties of linear elliptic operators/PDEs. In many studies and applications, it is important that such properties are preserved by the selected numerical solution method. In this paper we present and analyze the properties of positive approximations of $\cal A^{-\alpha}$ obtained by the BURA technique. Sufficient conditions for positiveness are proven, complemented by sharp error estimates. The theoretical results are supported by representative numerical tests