Fourier-based Function Secret Sharing with General Access Structure

Function secret sharing (FSS) scheme is a mechanism that calculates a function f(x) for x in {0,1}^n which is shared among p parties, by using distributed functions f_i:{0,1}^n -> G, where G is an Abelian group, while the function f:{0,1}^n -> G is kept secret to the parties. Ohsawa et al. in 2017 observed that any function f can be described as a linear combination of the basis functions by regarding the function space as a vector space of dimension 2^n and gave new FSS schemes based on the Fourier basis. All existing FSS schemes are of (p,p)-threshold type. That is, to compute f(x), we have to collect f_i(x) for all the distributed functions. In this paper, as in the secret sharing schemes, we consider FSS schemes with any general access structure. To do this, we observe that Fourier-based FSS schemes by Ohsawa et al. are compatible with linear secret sharing scheme. By incorporating the techniques of linear secret sharing with any general access structure into the Fourier-based FSS schemes, we show Fourier-based FSS schemes with any general access structure.Comment: 12 page

Light with tunable non-Markovian phase imprint

We introduce a simple and flexible method to generate spatially non-Markovian light with tunable coherence properties in one and two dimensions. The unusual behavior of this light is demonstrated experimentally by probing the far field and recording its diffraction pattern after a double slit: In both cases we observe instead of a central intensity maximum a line or cross shaped dark region, whose width and profile depend on the non-Markovian coherence properties. Since these properties can be controlled and easily reproduced in experiment, the presented approach lends itself to serve as a testbed to gain a deeper understanding of non-Markovian processes

Settling Some Open Problems on 2-Player Symmetric Nash Equilibria

Over the years, researchers have studied the complexity of several decision versions of Nash equilibrium in (symmetric) two-player games (bimatrix games). To the best of our knowledge, the last remaining open problem of this sort is the following; it was stated by Papadimitriou in 2007: find a non-symmetric Nash equilibrium (NE) in a symmetric game. We show that this problem is NP-complete and the problem of counting the number of non-symmetric NE in a symmetric game is #P-complete. In 2005, Kannan and Theobald defined the "rank of a bimatrix game" represented by matrices (A, B) to be rank(A+B) and asked whether a NE can be computed in rank 1 games in polynomial time. Observe that the rank 0 case is precisely the zero sum case, for which a polynomial time algorithm follows from von Neumann's reduction of such games to linear programming. In 2011, Adsul et. al. obtained an algorithm for rank 1 games; however, it does not solve the case of symmetric rank 1 games. We resolve this problem

Improving results of pediatric renal transplantation

BACKGROUND: Outcome after renal transplantation in children has been variable. We undertook a retrospective study of our experience over the past five years. STUDY DESIGN: From January 1, 1988, to October 15, 1992, 60 renal transplantations were performed upon 59 children at the Children's Hospital of Pittsburgh. Twenty-eight (47 percent) of the kidneys were from cadaveric donors, and 32 (53 percent) were from living donors. The recipients ranged in age from 0.8 to 17.4 years, with a mean of 9.8 ± 4.8 years. Forty-six (77 percent) recipients were undergoing a first transplant, while 14 (23 percent) received a second or third transplant. Eight (13 percent) of the patients were sensitized, with a panel reactive antibody of more than 40 percent. Eleven of the 14 patients undergoing retransplantation and seven of the eight patients who were sensitized received kidneys from cadaveric donors. Thirty- three (55 percent) patients received cyclosporine-based immunosuppression, and 27 (45 percent) received FK506 as the primary immunosuppressive agent. RESULTS: The median follow-up period was 36 months, with a range of six to 63 months. The one- and four-year actuarial patient survival rate was 100 and 98 percent. The one- and four-year actuarial graft survival rate was 98 and 83 percent. For living donor recipients, the one- and four-year actuarial patient survival rate was 100 and 100 percent; for cadaveric recipients, it was 100 and 96 percent. Corresponding one- and four-year actuarial graft survival rates were 100 and 95 percent for the living donor recipients and 96 and 69 percent for the cadaveric recipients. Patients on cyclosporine had a one- and four-year patient survival rate of 100 and 97 percent, and patients on FK506 had a one- and three-year patient survival rate of 100 and 100 percent. Corresponding one- and four-year actuarial graft survival rates were 100 and 85 percent in the cyclosporine group, while one- and three-year actuarial graft survival rates were 96 and 84 percent in the FK506 group. The mean serum creatinine level was 1.24 ± 0.64 mg per dL; the blood urea nitrogen level was 26 ± 13 mg per dL. The incidence of rejection was 47 percent; 75 percent of the rejections were steroid-responsive. The incidence of cytomegalovirus was 10 percent. The incidence of post-transplant lymphoproliferative disorder was 8 percent. None of the patients on cyclosporine were able to be taken off prednisone; 56 percent of the patients receiving FK506 were taken off prednisone successfully. Early growth and development data suggest that the patients receiving FK506 off prednisone had significant gains in growth. CONCLUSIONS: These results support the idea that renal transplantation is a successful therapy for end-stage renal disease in children. They also illustrate the potential benefits of a new immunosuppressive agent, FK506

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

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

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

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

Development of the Fetal Vermis: New Biometry Reference Data and Comparison of 3 Diagnostic Modalities-3D Ultrasound, 2D Ultrasound, and MR Imaging

Normal biometry of the fetal posterior fossa rules out most major anomalies of the cerebellum and vermis. Our aim was to provide new reference data of the fetal vermis in 4 biometric parameters by using 3 imaging modalities, 2D ultrasound, 3D ultrasound, and MR imaging, and to assess the relation among these modalities. A retrospective study was conducted between June 2011 and June 2013. Three different imaging modalities were used to measure vermis biometry: 2D ultrasound, 3D ultrasound, and MR imaging. The vermian parameters evaluated were the maximum superoinferior diameter, maximum anteroposterior diameter, the perimeter, and the surface area. Statistical analysis was performed to calculate centiles for gestational age and to assess the agreement among the 3 imaging modalities. The number of fetuses in the study group was 193, 172, and 151 for 2D ultrasound, 3D ultrasound, and MR imaging, respectively. The mean and median gestational ages were 29.1 weeks, 29.5 weeks (range, 21-35 weeks); 28.2 weeks, 29.05 weeks (range, 21-35 weeks); and 32.1 weeks, 32.6 weeks (range, 27-35 weeks) for 2D ultrasound, 3D ultrasound, and MR imaging, respectively. In all 3 modalities, the biometric measurements of the vermis have shown a linear growth with gestational age. For all 4 biometric parameters, the lowest results were those measured by MR imaging, while the highest results were measured by 3D ultrasound. The inter- and intraobserver agreement was excellent for all measures and all imaging modalities. Limits of agreement were considered acceptable for clinical purposes for all parameters, with excellent or substantial agreement defined by the intraclass correlation coefficient. Imaging technique-specific reference data should be used for the assessment of the fetal vermis in pregnanc