arXiv subjects

Daniel Miller

Publications and source records attributed to Daniel Miller.

25 records · Page 2Linked to original sources

arXiv2018

Direct measurement of Bacon-Shor code stabilizers

A Bacon-Shor code is a subsystem quantum error-correcting code on an $L \times L$ lattice where the $2(L-1)$ weight-$2L$ stabilizers are usually inferred from the measurements of $(L-1)^2$ weight-2 gauge operators. Here we show that the stabilizers can be measured directly and fault tolerantly with bare ancillary qubits by constructing circuits that follow the pattern of gauge operators. We then examine the implications of this method for small quantum error-correcting codes by comparing distance 3 versions of the rotated surface code and the Bacon-Shor code with the standard depolarizing model and in the context of a trapped ion quantum computer. We find that for a simple circuit of prepare, error correct and measure the Bacon-Shor code outperforms the surface code by requiring fewer qubits, taking less time, and having a lower error rate.

quant-ph↗

arXiv2017

Mg II Absorption at 2<z<7 with Magellan/FIRE, III. Full Statistics of Absorption Towards 100 High-Redshift QSOs

We present final statistics from a survey for intervening MgII absorption towards 100 quasars with emission redshifts between $z=3.55$ and $z=7.08$. Using infrared spectra from Magellan/FIRE, we detect 279 cosmological MgII absorbers, and confirm that the incidence rate of $W_r>0.3 Å$ MgII absorption per comoving path length does not evolve measurably between $z=0.25$ and $z=7$. This is consistent with our detection of seven new MgII systems at $z>6$, a redshift range that was not covered in prior searches. Restricting to relatively strong MgII systems ($W_r>1$Å), there is significant evidence for redshift evolution. These systems roughly double in number density between $z=0$ and $z=2$-$3$, but decline by an order of magnitude from this peak by $z\sim 6$. This evolution mirrors that of the global star formation rate density, which could reflect a connection between star formation feedback and strong MgII absorbers. We compared our results to the Illustris cosmological simulation at $z=2$-$4$ by assigning absorption to catalogued dark-matter halos and by direct extraction of spectra from the simulation volume. To reproduce our results using the halo catalogs, we require circumgalactic (CGM) MgII envelopes within halos of progressively smaller mass at earlier times. This occurs naturally if we define the lower integration cutoff using SFR rather than mass. MgII profiles calculated directly from the Illustris volume yield far too few strong absorbers. We argue that this arises from unresolved phase space structure of CGM gas, particularly from turbulent velocities on sub-mesh scales. The presence of CGM MgII at $z>6$-- just $\sim 250$ Myr after the reionization redshift implied by Planck--suggests that enrichment of intra-halo gas may have begun before the presumed host galaxies' stellar populations were mature and dynamically relaxed. [abridged]

astro-ph.CO↗

arXiv2017

Automated Identification of Drug-Drug Interactions in Pediatric Congestive Heart Failure Patients

Congestive Heart Failure, or CHF, is a serious medical condition that can result in fluid buildup in the body as a result of a weak heart. When the heart can't pump enough blood to efficiently deliver nutrients and oxygen to the body, kidney function may be impaired, resulting in fluid retention. CHF patients require a broad drug regimen to maintain the delicate system balance, particularly between their heart and kidneys. These drugs include ACE inhibitors and Beta Blockers to control blood pressure, anticoagulants to prevent blood clots, and diuretics to reduce fluid overload. Many of these drugs may interact, and potential effects of these interactions must be weighed against their benefits. For this project, we consider a set of 44 drugs identified as specifically relevant for treating CHF by pediatric cardiologists at Lucile Packard Children's Hospital. This list was generated as part of our current work at the LPCH Heart Center. The goal of this project is to identify and evaluate potentially harmful drug-drug interactions (DDIs) within pediatric patients with Congestive Heart Failure. This identification will be done autonomously, so that it may continuously update by evaluating newly published literature.

cs.CL↗

arXiv2015

The MegaFace Benchmark: 1 Million Faces for Recognition at Scale

Recent face recognition experiments on a major benchmark LFW show stunning performance--a number of algorithms achieve near to perfect score, surpassing human recognition rates. In this paper, we advocate evaluations at the million scale (LFW includes only 13K photos of 5K people). To this end, we have assembled the MegaFace dataset and created the first MegaFace challenge. Our dataset includes One Million photos that capture more than 690K different individuals. The challenge evaluates performance of algorithms with increasing numbers of distractors (going from 10 to 1M) in the gallery set. We present both identification and verification performance, evaluate performance with respect to pose and a person's age, and compare as a function of training data size (number of photos and people). We report results of state of the art and baseline algorithms. Our key observations are that testing at the million scale reveals big performance differences (of algorithms that perform similarly well on smaller scale) and that age invariant recognition as well as pose are still challenging for most. The MegaFace dataset, baseline code, and evaluation scripts, are all publicly released for further experimentations at: megaface.cs.washington.edu.

cs.CV↗

arXiv2015

The Structure of Divisible Abelian Groups

This is an expository work presenting in detail the proof of the structure theorem for divisible abelian groups. A divisible abelian group is an abelian group that satisfies nD=D for all natural n. The theorem states that any divisible group is a direct sum of copies of the additive rationals and quasicyclic groups.

math.GR↗

arXiv2014

Polygonal equalities and virtual degeneracy in $L_{p}$-spaces

Suppose $0 < p \leq 2$ and that $(Ω, μ)$ is a measure space for which $L_{p}(Ω, μ)$ is at least two-dimensional. The central results of this paper provide a complete description of the subsets of $L_{p}(Ω, μ)$ that have strict $p$-negative type. In order to do this we study non-trivial $p$-polygonal equalities in $L_{p}(Ω, μ)$. These are equalities that can, after appropriate rearrangement and simplification, be expressed in the form \begin{eqnarray*} \sum\limits_{j, i = 1}^{n} α_{j} α_{i} {\| z_{j} - z_{i} \|}_{p}^{p} & = & 0 \end{eqnarray*} where $\{ z_{1}, \ldots, z_{n} \}$ is a subset of $L_{p}(Ω, μ)$ and $α_{1}, \ldots, α_{n}$ are non-zero real numbers that sum to zero. We provide a complete classification of the non-trivial $p$-polygonal equalities in $L_{p}(Ω, μ)$. The cases $p < 2$ and $p = 2$ are substantially different and are treated separately. The case $p = 1$ generalizes an elegant result of Elsner, Han, Koltracht, Neumann and Zippin. Another reason for studying non-trivial $p$-polygonal equalities in $L_{p}(Ω, μ)$ is due to the fact that they preclude the existence of certain types of isometry. For example, our techniques show that if $(X,d)$ is a metric space that has strict $q$-negative type for some $q \geq p$, then: (1) $(X,d)$ is not isometric to any linear subspace $W$ of $L_{p}(Ω, μ)$ that contains a pair of disjointly supported non-zero vectors, and (2) $(X,d)$ is not isometric to any subset of $L_{p}(Ω, μ)$ that has non-empty interior. Furthermore, in the case $p = 2$, it also follows that $(X,d)$ is not isometric to any affinely dependent subset of $L_{2}(Ω, μ)$.

math.FA↗

arXiv2011

Strongly non embeddable metric spaces

Enflo constructed a countable metric space that may not be uniformly embedded into any metric space of positive generalized roundness. Dranishnikov, Gong, Lafforgue and Yu modified Enflo's example to construct a locally finite metric space that may not be coarsely embedded into any Hilbert space. In this paper we meld these two examples into one simpler construction. The outcome is a locally finite metric space $(\mathfrak{Z}, ζ)$ which is strongly non embeddable in the sense that it may not be embedded uniformly or coarsely into any metric space of non zero generalized roundness. Moreover, we show that both types of embedding may be obstructed by a common recursive principle. It follows from our construction that any metric space which is Lipschitz universal for all locally finite metric spaces may not be embedded uniformly or coarsely into any metric space of non zero generalized roundness. Our construction is then adapted to show that the group $\mathbb{Z}_ω=\bigoplus_{\aleph_0}\mathbb{Z}$ admits a Cayley graph which may not be coarsely embedded into any metric space of non zero generalized roundness. Finally, for each $p \geq 0$ and each locally finite metric space $(Z,d)$, we prove the existence of a Lipschitz injection $f : Z \to \ell_{p}$.

math.FA↗