Parts of Quantum States

It is shown that generic N-party pure quantum states (with equidimensional subsystems) are uniquely determined by their reduced states of just over half the parties; in other words, all the information in almost all N-party pure states is in the set of reduced states of just over half the parties. For N even, the reduced states in fewer than N/2 parties are shown to be an insufficient description of almost all states (similar results hold when N is odd). It is noted that Real Algebraic Geometry is a natural framework for any analysis of parts of quantum states: two simple polynomials, a quadratic and a cubic, contain all of their structure. Algorithmic techniques are described which can provide conditions for sets of reduced states to belong to pure or mixed states.Comment: 10 pages, 1 figur

Information Markets: A Research Landscape

Information markets are mechanisms that allow a group of geographically dispersed participants to reach and continuously reevaluate consensus by discovering the value of alternative outcomes. Evidence suggests that these markets can produce better quality decisions than a small subset of selected decision makers: a finding in direct opposition to the trust we place on expertise. In challenging and uncertain decision-making arenas, information markets offer an interesting, and somewhat counter-intuitive approach. In practice, information markets may be used in combination with other decision-making methods, but these market-based mechanisms offer many advantages. This paper presents an information market typology and explores some of the challenges raised by different market applications. Market types include event and estimation-based prediction markets, decision markets, and idea markets. An integrated research landscape model and research propositions are presented to help guide continuing research in this area

General moments of the inverse real Wishart distribution and orthogonal Weingarten functions

Let $W$ be a random positive definite symmetric matrix distributed according to a real Wishart distribution and let $W^{-1}=(W^{ij})_{i,j}$ be its inverse matrix. We compute general moments $\mathbb{E} [W^{k_1 k_2} W^{k_3 k_4} ... W^{k_{2n-1}k_{2n}}]$ explicitly. To do so, we employ the orthogonal Weingarten function, which was recently introduced in the study for Haar-distributed orthogonal matrices. As applications, we give formulas for moments of traces of a Wishart matrix and its inverse.Comment: 29 pages. The last version differs from the published version, but it includes Appendi

Polarization Requirements for Ensemble Implementations of Quantum Algorithms with a Single Bit Output

We compare the failure probabilities of ensemble implementations of quantum algorithms which use pseudo-pure initial states, quantified by their polarization, to those of competing classical probabilistic algorithms. Specifically we consider a class algorithms which require only one bit to output the solution to problems. For large ensemble sizes, we present a general scheme to determine a critical polarization beneath which the quantum algorithm fails with greater probability than its classical competitor. We apply this to the Deutsch-Jozsa algorithm and show that the critical polarization is 86.6%.Comment: 11 pages, 3 figure

AIDS orphans: The psychological adjustment of children with multiple family members with a terminal illness.

Fifty-two uninfected children of HIV positive women who had a sibling who was followed by the Pediatric AIDS Clinic at a large mid-Atlantic urban pediatric medical center participated in this study. Children ranged from 6-16 years of age (M = 10.29, SD = 3.25). Four separate measures were used; three were completed by the uninfected sibling: The Children's Depression Inventory (CDI), the Revised Children's Manifest Anxiety Scale (RCMAS), and the Kidcope. The remaining measure, the Child Behavior Checklist (CBCL), was completed by the caregiver. Descriptive statistics and multiple regression analyses were performed to test the theoretical model of adjustment created to assess the emotional adjustment of children who have multiple family members diagnosed with HIV/AIDS. As a group, these children were characterized by clinically elevated levels of psychological distress. Specifically, children who have experienced an HIV/AIDS related death in their family, have had their parent's or sibling's diagnosis disclosed to them, have a lack of available social supports and/or lack a stable living environment are at greater risk for developing behavioral and/or emotional problems.The rise in the number of Acquired Immune Deficiency Syndrome cases has created a new demographic in society, uninfected children with terminally ill family members. The uninfected children in HIV affected families may be exposed to a series of major psychological risk factors--stigma, secrecy, exposure to acute and chronic illness, death of parents and/or siblings, separations, losses, orphanhood and foster home placements. The purpose of this study was to assess the emotional adjustment of children who have multiple family members diagnosed with an Acquired Immune Deficiency Syndrome (AIDS)/Human Immunodeficiency Virus (HIV). Specifically, descriptive data was collected to determine the degree of relationship among various combinations of the predictor variables (knowledge of parent/sibling illness, previous death experiences, participation in choosing future living situation, social support, and a history of a stable living situation) and each of the dependent measures

Evaluating survey methods for bat roost detection in ecological impact assessment

International audienceThe disturbance, damage and destruction of roosts are key drivers of bat population declines worldwide. In countries where bats are protected by law, bat roost surveys are often required to inform ecological impact assessments. Yet, evidence-based information on survey methodology to detect bat roosts is crucially lacking, and failing to detect a roost can lead to serious errors during decision-making processes. Here, we assess the efficacy of bat roost surveys in buildings as implemented in the UK. These consist of a daytime inspection of buildings, followed by a series of acoustic surveys at dusk/dawn if during the daytime inspection evidence of bats is found, or if the absence of bats cannot be verified. We reviewed 155 ecological consultants’ reports to (1) compare survey outcome between daytime inspection and acoustic surveys and (2) determine the minimum sampling effort required during acoustic surveys to be confident that no bats are roosting within a building. We focused on two genera of bats most frequently found in buildings in Europe – Pipistrellus (crevice roosting species with high-intensity echolocation calls that can be easily detected by ultrasound detectors) and Plecotus (species that roost in open spaces and which emit faint echolocation calls that are difficult to detect). Daytime inspections were efficient in detecting open-roosting species such as Plecotus species but were likely to miss the presence of crevice-dwelling ones (here Pipistrellus species) which may lead to erroneous conclusions if no acoustic surveys are subsequently prescribed to confirm their absence. A minimum of three and four acoustic surveys are required to be 95% confident that a building does not host a roost of Pipistrellus species and Plecotus species, respectively, thus exceeding current recommendations. Overall, we demonstrated that reports submitted as part of an ecological impact assessment provide suitable data to test and improve survey methods

Reliability and similarity of resting state functional connectivity networks imaged using wearable, high-density diffuse optical tomography in the home setting

Background: When characterizing the brain's resting state functional connectivity (RSFC) networks, demonstrating networks' similarity across sessions and reliability across different scan durations is essential for validating results and possibly minimizing the scanning time needed to obtain stable measures of RSFC. Recent advances in optical functional neuroimaging technologies have resulted in fully wearable devices that may serve as a complimentary tool to functional magnetic resonance imaging (fMRI) and allow for investigations of RSFC networks repeatedly and easily in non-traditional scanning environments. Methods: Resting-state cortical hemodynamic activity was repeatedly measured in a single individual in the home environment during COVID-19 lockdown conditions using the first ever application of a 24-module (72 sources, 96 detectors) wearable high-density diffuse optical tomography (HD-DOT) system. Twelve-minute recordings of resting-state data were acquired over the pre-frontal and occipital regions in fourteen experimental sessions over three weeks. As an initial validation of the data, spatial independent component analysis was used to identify RSFC networks. Reliability and similarity scores were computed using metrics adapted from the fMRI literature. Results: We observed RSFC networks over visual regions (visual peripheral, visual central networks) and higher-order association regions (control, salience and default mode network), consistent with previous fMRI literature. High similarity was observed across testing sessions and across chromophores (oxygenated and deoxygenated haemoglobin, HbO and HbR) for all functional networks, and for each network considered separately. Stable reliability values (described here as a <10% change between time windows) were obtained for HbO and HbR with differences in required scanning time observed on a network-by-network basis. Discussion: Using RSFC data from a highly sampled individual, the present work demonstrates that wearable HD-DOT can be used to obtain RSFC measurements with high similarity across imaging sessions and reliability across recording durations in the home environment. Wearable HD-DOT may serve as a complimentary tool to fMRI for studying RSFC networks outside of the traditional scanning environment and in vulnerable populations for whom fMRI is not feasible

Heteroleptic Calcium Complexes Supported by a Phenoxy-Imine NON Ligand: Polymerization of Cyclic Esters by a Ligand-Assisted, Activated-Monomer Mechanism

Phenoxy-imine NON pro-ligands HR,DippL [1-OH-2,6-(HCNDipp)-4-R-C6H2, where R = H, Me, or t Bu] were deprotonated using KH to afford the corresponding potassium salts R,DippLK·thf x [R = H (1·thf x ), Me (2·thf x ), and t Bu (3·thf x )]. The addition of crown ether (18-c-6) to these salts allowed for the structures of the resulting adducts to be elucidated in the solid state: [1­(18-c-6)] n , [2­(18-c-6)] n , and [3­(18-c-6)­(thf)]. The derivatives with the smaller para-substituents were found to be 1D coordination polymers stabilized by unusual non-covalent interactions between the diisopropyl-methyl groups and the potassium center. Heteroleptic calcium complexes R,DippLCaI­(thf)3 [R = H (4), Me (5), and t Bu (6)] were prepared by the salt metathesis reaction of 1–3·thf x with CaI2. Complexes 4–6 were evaluated as initiators for the ring-opening polymerization of lactide monomers and were all found to be active; the addition of benzyl alcohol resulted in large rate increases, e.g., ∼12-fold difference for 6 (0.70 vs 0.06 h–1). The propagation rate constants were found to lie within the range 88–135 M–1 h–1. Variation of co-initiator concentration revealed only a fractional dependence; this agrees with the other experimental observations, which suggest that the heteroleptic catalysts work via a “ligand-assisted, activated monomer” mechanism

Wearable HD-DOT for investigating functional connectivity in the adult brain: A single subject, multi-session study

We applied a wearable 24-module high-density diffuse optical tomography (HD-DOT) system in a resting state (RS) paradigm repeatedly in one subject. Seed-based correlation maps show large field-of-view RS functional connectivity