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

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

Experimental Heat-Bath Cooling of Spins

Algorithmic cooling (AC) is a method to purify quantum systems, such as ensembles of nuclear spins, or cold atoms in an optical lattice. When applied to spins, AC produces ensembles of highly polarized spins, which enhance the signal strength in nuclear magnetic resonance (NMR). According to this cooling approach, spin-half nuclei in a constant magnetic field are considered as bits, or more precisely, quantum bits, in a known probability distribution. Algorithmic steps on these bits are then translated into specially designed NMR pulse sequences using common NMR quantum computation tools. The $algorithmic$ cooling of spins is achieved by alternately combining reversible, entropy-preserving manipulations (borrowed from data compression algorithms) with $selective$ $reset$, the transfer of entropy from selected spins to the environment. In theory, applying algorithmic cooling to sufficiently large spin systems may produce polarizations far beyond the limits due to conservation of Shannon entropy. Here, only selective reset steps are performed, hence we prefer to call this process "heat-bath" cooling, rather than algorithmic cooling. We experimentally implement here two consecutive steps of selective reset that transfer entropy from two selected spins to the environment. We performed such cooling experiments with commercially-available labeled molecules, on standard liquid-state NMR spectrometers. Our experiments yielded polarizations that $bypass$ $Shannon's$ $entropy$-$conservation$ $bound$, so that the entire spin-system was cooled. This paper was initially submitted in 2005, first to Science and then to PNAS, and includes additional results from subsequent years (e.g. for resubmission in 2007). The Postscriptum includes more details.Comment: 20 pages, 8 figures, replaces quant-ph/051115

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

Multiclass Semi-Supervised Learning on Graphs using Ginzburg-Landau Functional Minimization

We present a graph-based variational algorithm for classification of high-dimensional data, generalizing the binary diffuse interface model to the case of multiple classes. Motivated by total variation techniques, the method involves minimizing an energy functional made up of three terms. The first two terms promote a stepwise continuous classification function with sharp transitions between classes, while preserving symmetry among the class labels. The third term is a data fidelity term, allowing us to incorporate prior information into the model in a semi-supervised framework. The performance of the algorithm on synthetic data, as well as on the COIL and MNIST benchmark datasets, is competitive with state-of-the-art graph-based multiclass segmentation methods.Comment: 16 pages, to appear in Springer's Lecture Notes in Computer Science volume "Pattern Recognition Applications and Methods 2013", part of series on Advances in Intelligent and Soft Computin

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