The Data Breach Dilemma: Proactive Solutions for Protecting Consumers’ Personal Information

Data breaches are an increasingly common part of consumers’ lives. No institution is immune to the possibility of an attack. Each breach inevitably risks the release of consumers’ personally identifiable information and the strong possibility of identity theft. Unfortunately, current solutions for handling these incidents are woefully inadequate. Private litigation like consumer class actions and shareholder lawsuits each face substantive legal and procedural barriers. States have their own data security and breach notification laws, but there is currently no unifying piece of legislation or strong enforcement mechanism. This Note argues that proactive solutions are required. First, a national data security law—setting minimum data security standards, regulating the use and storage of personal information, and expanding the enforcement role of the Federal Trade Commission—is imperative to protect consumers’ data. Second, a proactive solution requires reconsidering how to minimize the problem by going to its source: the collection of personally identifiable information in the first place. This Note suggests regulating companies’ collection of Social Security numbers, and, eventually, using a system based on distributed ledger technology to replace the ubiquity of Social Security numbers

Integrability and weak diffraction in a two-particle Bose-Hubbard model

A recently introduced one-dimensional two-particle Bose-Hubbard model with a single impurity is studied on finite lattices. The model possesses a discrete reflection symmetry and we demonstrate that all eigenstates odd under this symmetry can be obtained with a generalized Bethe ansatz if periodic boundary conditions are imposed. Furthermore, we provide numerical evidence that this holds true for open boundary conditions as well. The model exhibits backscattering at the impurity site -- which usually destroys integrability -- yet there exists an integrable subspace. We investigate the non-integrable even sector numerically and find a class of states which have almost the Bethe ansatz form. These weakly diffractive states correspond to a weak violation of the non-local Yang-Baxter relation which is satisfied in the odd sector. We bring up a method based on the Prony algorithm to check whether a numerically obtained wave function is in the Bethe form or not, and if so, to extract parameters from it. This technique is applicable to a wide variety of other lattice models.Comment: 13.5 pages, 11 figure

Bound states in the one-dimensional two-particle Hubbard model with an impurity

We investigate bound states in the one-dimensional two-particle Bose-Hubbard model with an attractive ($V> 0$) impurity potential. This is a one-dimensional, discrete analogy of the hydrogen negative ion H$^-$ problem. There are several different types of bound states in this system, each of which appears in a specific region. For given $V$, there exists a (positive) critical value $U_{c1}$ of $U$, below which the ground state is a bound state. Interestingly, close to the critical value ($U\lesssim U_{c1}$), the ground state can be described by the Chandrasekhar-type variational wave function, which was initially proposed for H$^-$. For $U>U_{c1}$, the ground state is no longer a bound state. However, there exists a second (larger) critical value $U_{c2}$ of $U$, above which a molecule-type bound state is established and stabilized by the repulsion. We have also tried to solve for the eigenstates of the model using the Bethe ansatz. The model possesses a global \Zz_2-symmetry (parity) which allows classification of all eigenstates into even and odd ones. It is found that all states with odd-parity have the Bethe form, but none of the states in the even-parity sector. This allows us to identify analytically two odd-parity bound states, which appear in the parameter regions $-2V<U<-V$ and $-V<U<0$, respectively. Remarkably, the latter one can be \textit{embedded} in the continuum spectrum with appropriate parameters. Moreover, in part of these regions, there exists an even-parity bound state accompanying the corresponding odd-parity bound state with almost the same energy.Comment: 18 pages, 18 figure

Bound States in the Continuum Realized in the One-Dimensional Two-Particle Hubbard Model with an Impurity

We report a bound state of the one-dimensional two-particle (bosonic or fermionic) Hubbard model with an impurity potential. This state has the Bethe-ansatz form, although the model is nonintegrable. Moreover, for a wide region in parameter space, its energy is located in the continuum band. A remarkable advantage of this state with respect to similar states in other systems is the simple analytical form of the wave function and eigenvalue. This state can be tuned in and out of the continuum continuously.Comment: A semi-exactly solvable model (half of the eigenstates are in the Bethe form

Error Estimates for Adaptive Spectral Decompositions

Adaptive spectral (AS) decompositions associated with a piecewise constant function, $u$, yield small subspaces where the characteristic functions comprising $u$ are well approximated. When combined with Newton-like optimization methods, AS decompositions have proved remarkably efficient in providing at each nonlinear iteration a low-dimensional search space for the solution of inverse medium problems. Here, we derive $L^2$-error estimates for the AS decomposition of $u$, truncated after $K$ terms, when $u$ is piecewise constant and consists of $K$ characteristic functions over Lipschitz domains and a background. Numerical examples illustrate the accuracy of the AS decomposition for media that either do, or do not, satisfy the assumptions of the theory

Adaptive spectral decompositions for inverse medium problems

Inverse medium problems involve the reconstruction of a spatially varying unknown medium from available observations by exploring a restricted search space of possible solutions. Standard grid-based representations are very general but all too often computationally prohibitive due to the high dimension of the search space. Adaptive spectral (AS) decompositions instead expand the unknown medium in a basis of eigenfunctions of a judicious elliptic operator, which depends itself on the medium. Here the AS decomposition is combined with a standard inexact Newton-type method for the solution of time-harmonic scattering problems governed by the Helmholtz equation. By repeatedly adapting both the eigenfunction basis and its dimension, the resulting adaptive spectral inversion (ASI) method substantially reduces the dimension of the search space during the nonlinear optimization. Rigorous estimates of the AS decomposition are proved for a general piecewise constant medium. Numerical results illustrate the accuracy and efficiency of the ASI method for time-harmonic inverse scattering problems, including a salt dome model from geophysics

Using The Barton Libraries Dataset As An RDF benchmark

This report describes the Barton Libraries RDF dataset and Longwell querybenchmark that we use for our recent VLDB paper on Scalable Semantic WebData Management Using Vertical Partitioning

Use Of Secondary Equilibria For The Separation Of Small Solutes By Field-Flow Fractionation

The dynamic range and selectivity of field-flow fractionation (FFF) can be Increased by using secondary chemical equilibria (SCE). SCE are established by adding a macromolecular additive or aggregate, which strongly Interacts with the field, to the carrier solution. In this study an oil-ln-water (O/W) microemulsion was used as the carrier solution in a sedimentation FFF apparatus. The microemulsion droplets (referred to as the support ) interact with the field and are retained relative to the bulk water. Small solutes that partition or bind to the microemulsion droplets are also retained relative to solutes that do not Interact with the support. In this way It Is possible to separate somewhat polar compounds, such as ascorbic acid and sodium benzoate, which prefer bulk water, from a polar solute, such as toluene, which prefers the support. In addition, the study of retention times in this system allows one to calculate the average microemulsion droplet radius. It appears that SCE-FFF could be a useful way to obtain Important Information on the physicochemical properties of a variety of colloidal supports. © 1988, American Chemical Society. All rights reserved