Unknown Ordering Research Articles

Multi-Analyst Differential Privacy for Online Query Answering

Most differentially private mechanisms are designed for the use of a single analyst. In reality, however, there are often multiple stakeholders with different and possibly conflicting priorities that must share the same privacy loss budget. This motivates the problem of equitable budget-sharing for multi-analyst differential privacy. Our previous work defined desiderata that any mechanism in this space should satisfy and introduced methods for budget-sharing in the offline case where queries are known in advance. We extend our previous work on multi-analyst differentially private query answering to the case of online query answering, where queries come in one at a time and must be answered without knowledge of the following queries. We demonstrate that the unknown ordering of queries in the online case results in a fundamental limit in the number of queries that can be answered while satisfying the desiderata. In response, we develop two mechanisms, one which satisfies the desiderata in all cases but is subject to the fundamental limitations, and another that randomizes the input order ensuring that existing online query answering mechanisms can satisfy the desiderata.

A pathway toward high-throughput quantum Monte Carlo simulations for alloys: A case study of two-dimensional (2D) GaSxSe1-x.

The study of alloys using computational methods has been a difficult task due to the usually unknown stoichiometry and local atomic ordering of the different structures experimentally. In order to combat this, first-principles methods have been coupled with statistical methods such as the cluster expansion formalism in order to construct the energy hull diagram, which helps to determine if an alloyed structure can exist in nature. Traditionally, density functional theory (DFT) has been used in such workflows. In this paper, we propose to use chemically accurate many-body variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC) methods to construct the energy hull diagram of an alloy system due to the fact that such methods have a weakerdependence on the starting wavefunction and density functional, scale similarly to DFT with the number of electrons, and have had demonstrated success for a variety of materials. To carry out these simulations in a high-throughput manner, we propose a method called Jastrow sharing, which involves recycling the optimized Jastrow parameters between alloys with different stoichiometries. We show that this eliminates the need for extra VMC Jastrow optimization calculations and results in significant computational cost savings (on average 1/4 savings of total computational time). Since it is a novel post-transition metal chalcogenide alloy series that has been synthesized in its few-layer form, we used monolayer GaSxSe1-x as a case study for our workflow. By extensively testing our Jastrow sharing procedure for monolayer GaSxSe1-x and quantifying the cost savings, we demonstrate how a pathway toward chemically accurate high-throughput simulations of alloys can be achieved using many-body VMC and DMC methods.

A benchmark for dose-finding studies with unknown ordering.

SummaryAn important tool to evaluate the performance of a dose-finding design is the nonparametric optimal benchmark that provides an upper bound on the performance of a design under a given scenario. A fundamental assumption of the benchmark is that the investigator can arrange doses in a monotonically increasing toxicity order. While the benchmark can be still applied to combination studies in which not all dose combinations can be ordered, it does not account for the uncertainty in the ordering. In this article, we propose a generalization of the benchmark that accounts for this uncertainty and, as a result, provides a sharper upper bound on the performance. The benchmark assesses how probable the occurrence of each ordering is, given the complete information about each patient. The proposed approach can be applied to trials with an arbitrary number of endpoints with discrete or continuous distributions. We illustrate the utility of the benchmark using recently proposed dose-finding designs for Phase I combination trials with a binary toxicity endpoint and Phase I/II combination trials with binary toxicity and continuous efficacy.

Stochastic on-time arrival problem in transit networks

This article considers the stochastic on-time arrival problem in transit networks where both the travel time and the waiting time for transit services are stochastic. A specific challenge of this problem is the combinatorial solution space due to the unknown ordering of transit line arrivals. We propose a network structure appropriate to the online decision-making of a passenger, including boarding, waiting and transferring. In this framework, we design a dynamic programming algorithm that is pseudo-polynomial in the number of transit stations and travel time budget, and exponential in the number of transit lines at a station, which is a small number in practice. To reduce the search space, we propose a definition of transit line dominance, and techniques to identify dominance, which decrease the computation time by up to 90% in numerical experiments. Extensive numerical experiments are conducted on both a synthetic network and the Chicago transit network.

Survival analysis of DNA mutation motifs with penalized proportional hazards.

Antibodies, an essential part of our immune system, develop through an intricate process to bind a wide array of pathogens. This process involves randomly mutating DNA sequences encoding these antibodies to find variants with improved binding, though mutations are not distributed uniformly across sequence sites. Immunologists observe this nonuniformity to be consistent with "mutation motifs", which are short DNA subsequences that affect how likely a given site is to experience a mutation. Quantifying the effect of motifs on mutation rates is challenging: a large number of possible motifs makes this statistical problem high dimensional, while the unobserved history of the mutation process leads to a nontrivial missing data problem. We introduce an ℓ 1-penalized proportional hazards model to infer mutation motifs and their effects. In order to estimate model parameters, our method uses a Monte Carlo EM algorithm to marginalize over the unknown ordering of mutations. We show that our method performs better on simulated data compared to current methods and leads to more parsimonious models. The application of proportional hazards to mutation processes is, to our knowledge, novel and formalizes the current methods in a statistical framework that can be easily extended to analyze the effect of other biological features on mutation rates.

Identification of the crossing point at N=21 between normal and intruder configurations

The β− decay of Mg34 was used to study the Al34 nucleus through γ spectroscopy at the Isotope Separator On-Line facility of CERN. Previous studies identified two β-decaying states in Al34 having spin-parity assignments Jπ=4− dominated by the normal configuration π(d5/2)−1⊗ν(f7/2) and Jπ=1+ by the intruder configuration π(d5/2)−1⊗ν(d3/2)−1(f7/2)2. Their unknown ordering and relative energy have been the subject of debate for the placement of Al34 inside or outside the N=20 “island of inversion.” We report here that the 1+ intruder lies only 46.6 keV above the 4− ground state. In addition, a new half-life of T1/2=44.9(4)ms, that is twice as long as the previously measured 20(10) ms, has been determined for Mg34. Large-scale shell-model calculations with the recently developed sdpf-u-mix interaction are compared with the new data and used to interpret the mechanisms at play at the very border of the N=20 island of inversion.

Formalisation of the multigrid computations

The paper represents a robust multigrid algorithm for solving a large class of applied problems from Poisson equation to Navier-Stokes equations on the structured grids. The algorithm consists of the robust multigrid technique variant of the geometric multigrid methods with the problem-independent transfer operators and the smoothing procedure based on Gauss-Seidel iterations with block unknown ordering. Theoretical analysis and numerical experiments show that close-to-optimal convergence rate for many nonlinear problems is obtained with the same multigrid components. Proposed approach can be used in black box software.

Rate Distortion Behavior of Sparse Sources

The rate distortion behavior of sparse memoryless sources is studied. These serve as models of sparse signal representations and facilitate the performance analysis of “sparsifying” transforms like the wavelet transform and nonlinear approximation schemes. For strictly sparse binary sources with Hamming distortion, R(D) is shown to be almost linear. For nonstrictly sparse continuous-valued sources, termed compressible, two measures of compressibility are introduced: incomplete moments and geometric mean. The former lead to low- and high-rate upper bounds on mean squared error D(R), while the latter yields lower and upper bounds on source entropy, thereby characterizing asymptotic R(D) behavior. Thus, the notion of compressibility is quantitatively connected with actual lossy compression. These bounding techniques are applied to two source models: Gaussian mixtures and power laws matching the approximately scale-invariant decay of wavelet coefficients. The former are versatile models for sparse data, which in particular allow to bound high-rate compression performance of a scalar mixture compared to a corresponding unmixed transform coding system. Such a comparison is interesting for transforms with known coefficient decay, but unknown coefficient ordering, e.g., when positions of highest-variance coefficients are unknown. The use of these models and results in distributed coding and compressed sensing scenarios are also discussed.

A survey on direct solvers for Galerkin methods

In this paper we describe the history, performance, and design concepts of direct solvers for algebraic systems resulting from Galerkin discretizations of partial differential equations. Popular direct solver implementations of Gaussian elimination (also known as LU factorization) are introduced and briefly analyzed. We discuss three of the most relevant aspects influencing the performance of direct solvers on this kind of algebraic systems. First, the ordering of the degrees of freedom of the algebraic system has a significant impact on the solver performance, solution speed and memory requirements. The impact of unknowns ordering for elimination is exemplified and alternative ordering algorithms are described and compared. Second, the effect of round-off error on the simulation results is discussed. We detail this effect for uniform grids where the impact of round-off error on the solution is controlled by the condition number of the matrix in terms of the element size, but is independent of the polynomial order of approximation. Additionally, we discuss the link between unknown ordering and round-off error. Third, we describe the impact of the connectivity pattern (graph) of the basis functions on the performance of direct solvers. Variations in the connectivity structure of the resulting discrete system have severe impact on performance of the solver. That is, the resources needed to factorize the system strongly depend on its connectivity graph. Less connected graphs are cheaper to solve, that is, C0 finite element discretizations are cheaper to solve with direct solvers than Cp−1 discretizations.

Mechanism of Dihydrouridine Synthase 2 from Yeast and the Importance of Modifications for Efficient tRNA Reduction

Dihydrouridine synthases (DUSs) are flavin-dependent enzymes that catalyze site-specific reduction of uracils in tRNAs. The mechanism of DUS 2 from Saccharomyces cerevisiae was studied. Previously published turnover rates for this DUS were very low. Our studies show that the catalytic cycle consists of reductive and oxidative half-reactions. The enzyme is reduced by NADPH rapidly but has a very slow oxidative half-reaction using in vitro transcribed tRNA substrates. Using tRNA(Leu) purified from a DUS 2 knockout strain of yeast we obtained reaction rate enhancements of 600-fold over in vitro transcribed substrates, indicating that other RNA modifications are required for rapid uracil reduction. This demonstrates a previously unknown ordering of modifications and indicates that dihydrouridine formation is a later step in tRNA maturation. We also show that an active site cysteine is important for catalysis, likely in the protonation of uracil during tRNA reduction. Dihydrouridine of modified tRNA from Escherichia coli was also oxidized to uridine showing the reaction to be reversible.

Specific heat ofURu2Si2in fields up to 42 T: Clues to the hidden order

The large $\Delta$C observed at 17.5 K in URu$_{2}$Si$_{2}$ is inconsistent with the small, 0.04 $\mu_{B}$ moment measured for the antiferromagnetism observed starting (perhaps coincidentally) at the same temperature. We report measurements of this specific heat transition, thought to be due to some 'hidden order', in magnetic fields between 24 and 42 T, i. e. through the field region where three metamagnetic transtions are known to occur at 35.8, 37.3, and 39.4 T. The response of $\Delta$C in single crystal URu$_{2}$Si$_{2}$ to magnetic field, which includes a change to $\Delta$C being possibly associated with a first order phase transition for high fields, is analyzed to shed further light on the possible explanations of this unknown ordering process. At fields above 35 T, a new high field phase comes into being; the connection between this high field phase revealed by the specific heat and earlier magnetization data is discussed.

A note on the nonmetric analysis of psychological intervals for an unknown ordering of stimuli

A modified version of a coordinate adjustment technique which permits the analysis of comparisons of psychological intervals for an unknown ordering of stimuli is described and compared to the original version and to TORSCA. For configurations with a large number of points, knowledge of the rank order of the stimuli does not improve the solution. For configurations with a small number of points, the performance of the new algorithm with an unknown ordering is equivalent to TORSCA.

The XYZ Conjecture and the FKG Inequality

Consider random variables $x_1, \cdots, x_n$, independently and uniformly distributed on the unit interval. Suppose we are given partial information, $\Gamma$, about the unknown ordering of the $x$'s; e.g., $\Gamma = \{x_1 < x_{12}, x_7 < x_5, \cdots\}$. We prove the "XYZ conjecture" (originally due to Ivan Rival, Bill Sands, and extended by Peter Winkler, R. L. Graham, and other participants of the Symposium on Ordered Sets at Banff, 1981) that $P(x_1 < x_2|\Gamma) \leq P(x_1 < x_2|\Gamma, x_1 < x_3).$ The proof is based on the FKG inequality for correlations and shows by example that even when the hypothesis of the FKG inequality fails it may be possible to redefine the partial ordering so that the conclusion of the FKG inequality still holds.