Pseudorandom Generators for Width-3 Branching Programs

We construct pseudorandom generators of seed length $\tilde{O}(\log(n)\cdot \log(1/\epsilon))$ that $\epsilon$-fool ordered read-once branching programs (ROBPs) of width $3$ and length $n$. For unordered ROBPs, we construct pseudorandom generators with seed length $\tilde{O}(\log(n) \cdot \mathrm{poly}(1/\epsilon))$. This is the first improvement for pseudorandom generators fooling width $3$ ROBPs since the work of Nisan [Combinatorica, 1992]. Our constructions are based on the `iterated milder restrictions' approach of Gopalan et al. [FOCS, 2012] (which further extends the Ajtai-Wigderson framework [FOCS, 1985]), combined with the INW-generator [STOC, 1994] at the last step (as analyzed by Braverman et al. [SICOMP, 2014]). For the unordered case, we combine iterated milder restrictions with the generator of Chattopadhyay et al. [CCC, 2018]. Two conceptual ideas that play an important role in our analysis are: (1) A relabeling technique allowing us to analyze a relabeled version of the given branching program, which turns out to be much easier. (2) Treating the number of colliding layers in a branching program as a progress measure and showing that it reduces significantly under pseudorandom restrictions. In addition, we achieve nearly optimal seed-length $\tilde{O}(\log(n/\epsilon))$ for the classes of: (1) read-once polynomials on $n$ variables, (2) locally-monotone ROBPs of length $n$ and width $3$ (generalizing read-once CNFs and DNFs), and (3) constant-width ROBPs of length $n$ having a layer of width $2$ in every consecutive $\mathrm{poly}\log(n)$ layers.Comment: 51 page

Is the direct observation of electronic coherence in electron transfer reactions possible?

The observability of electronic coherence in electron transfer reactions is discussed. We show that under appropriate circumstances large-amplitude oscillations can be found in the electronic occupation probabilities. The initial preparation of the system is of crucial importance for this effect, and we discuss conditions under which experiments detecting electronic coherence should be feasible. The Feynman-Vernon influence functional formalism is extended to examine more general and experimentally relevant initial preparations. Analytical expressions and path integral quantum dynamics simulations were developed to study the effects of various initial preparations on the observability of electronic coherence.Comment: 14 pages, 9 figures, to be published in J. Chem. Phy

Constraint Satisfaction with Counting Quantifiers

We initiate the study of constraint satisfaction problems (CSPs) in the presence of counting quantifiers, which may be seen as variants of CSPs in the mould of quantified CSPs (QCSPs). We show that a single counting quantifier strictly between exists^1:=exists and exists^n:=forall (the domain being of size n) already affords the maximal possible complexity of QCSPs (which have both exists and forall), being Pspace-complete for a suitably chosen template. Next, we focus on the complexity of subsets of counting quantifiers on clique and cycle templates. For cycles we give a full trichotomy -- all such problems are in L, NP-complete or Pspace-complete. For cliques we come close to a similar trichotomy, but one case remains outstanding. Afterwards, we consider the generalisation of CSPs in which we augment the extant quantifier exists^1:=exists with the quantifier exists^j (j not 1). Such a CSP is already NP-hard on non-bipartite graph templates. We explore the situation of this generalised CSP on bipartite templates, giving various conditions for both tractability and hardness -- culminating in a classification theorem for general graphs. Finally, we use counting quantifiers to solve the complexity of a concrete QCSP whose complexity was previously open

Invasive Haemophilus influenzae Disease in Adults ≥65 Years, United States, 2011.

BackgroundSince the introduction of the Haemophilus influenzae serotype b vaccine, H influenzae epidemiology has shifted. In the United States, the largest burden of disease is now in adults aged ≥65 years. However, few data exist on risk factors for disease severity and outcome in this age group.MethodsA retrospective case-series review of invasive H influenzae infections in patients aged ≥65 years was conducted for hospitalized cases reported to Active Bacterial Core surveillance in 2011.ResultsThere were 299 hospitalized cases included in the analysis. The majority of cases were caused by nontypeable H influenzae, and the overall case fatality ratio (CFR) was 19.5%. Three or more underlying conditions were present in 63% of cases; 94% of cases had at least 1. Patients with chronic heart conditions (congestive heart failure, coronary artery disease, and/or atrial fibrillation) (odds ratio [OR], 3.27; 95% confidence interval [CI], 1.65-6.46), patients from private residences (OR, 8.75; 95% CI, 2.13-35.95), and patients who were not resuscitate status (OR, 2.72; 95% CI, 1.31-5.66) were more likely to be admitted to the intensive care unit (ICU). Intensive care unit admission (OR, 3.75; 95% CI, 1.71-8.22) and do not resuscitate status (OR, 12.94; 95% CI, 4.84-34.55) were significantly associated with death.ConclusionsWithin this age group, burden of disease and CFR both increased significantly as age increased. Using ICU admission as a proxy for disease severity, our findings suggest several conditions increased risk of disease severity and patients with severe disease were more likely to die. Further research is needed to determine the most effective approach to prevent H influenzae disease and mortality in older adults

Meningococcal Disease in Patients With Human Immunodeficiency Virus Infection: A Review of Cases Reported Through Active Surveillance in the United States, 2000-2008.

BackgroundAlthough human immunodeficiency virus (HIV) infection is an established risk factor for several bacterial infections, the association between HIV infection and meningococcal disease remains unclear.MethodsExpanded chart reviews were completed on persons with meningococcal disease and HIV infection reported from 2000 through 2008 from 9 US sites participating in an active population-based surveillance system for meningococcal disease. The incidence of meningococcal disease among patients meeting Centers for Disease Control and Prevention acquired immune deficiency syndrome (AIDS) surveillance criteria was estimated using data from the National HIV Surveillance System for the participating sites.ResultsThirty-three cases of meningococcal disease in individuals with HIV infection were reported from participating sites, representing 2.0% of all reported meningococcal disease cases. Most (75.8%) persons with HIV infection were adult males aged 25 to 64 years old. Among all meningococcal disease cases aged 25 to 64 years old, case fatality ratios were similar among HIV-infected and HIV-uninfected persons (13.3% vs 10.6%; P = .6). The cumulative, mean incidence of meningococcal disease among patients aged 25 to 64 years old with HIV infection ever classified as AIDS was 3.5 cases per 100000 person years (95% confidence interval [CI], 2.1-5.6), compared with 0.3 cases per 100000 person years (95% CI, 0.3-0.3) for persons of the same age group not reported to have AIDS (relative risk = 12.9; 95% CI, 7.9-20.9).ConclusionsIndividuals with HIV infection meeting the AIDS surveillance case definition have a higher incidence of meningococcal disease compared with the general adult population

From Low-Distortion Norm Embeddings to Explicit Uncertainty Relations and Efficient Information Locking

The existence of quantum uncertainty relations is the essential reason that some classically impossible cryptographic primitives become possible when quantum communication is allowed. One direct operational manifestation of these uncertainty relations is a purely quantum effect referred to as information locking. A locking scheme can be viewed as a cryptographic protocol in which a uniformly random n-bit message is encoded in a quantum system using a classical key of size much smaller than n. Without the key, no measurement of this quantum state can extract more than a negligible amount of information about the message, in which case the message is said to be "locked". Furthermore, knowing the key, it is possible to recover, that is "unlock", the message. In this paper, we make the following contributions by exploiting a connection between uncertainty relations and low-distortion embeddings of L2 into L1. We introduce the notion of metric uncertainty relations and connect it to low-distortion embeddings of L2 into L1. A metric uncertainty relation also implies an entropic uncertainty relation. We prove that random bases satisfy uncertainty relations with a stronger definition and better parameters than previously known. Our proof is also considerably simpler than earlier proofs. We apply this result to show the existence of locking schemes with key size independent of the message length. We give efficient constructions of metric uncertainty relations. The bases defining these metric uncertainty relations are computable by quantum circuits of almost linear size. This leads to the first explicit construction of a strong information locking scheme. Moreover, we present a locking scheme that is close to being implementable with current technology. We apply our metric uncertainty relations to exhibit communication protocols that perform quantum equality testing.Comment: 60 pages, 5 figures. v4: published versio