A (v,k,lambda) -difference set in a group G of order v is a subset {d(1),d(2),& mldr;,d(k)} of G such that D = & sum;d(i) in the group ring Z[G] satisfies: DD-1=n+lambda G , where n=k-lambda . In other words, the nonzero elements of G all occur exactly lambda times as differences of elements in D. A (v,k,lambda,t) -almost difference set has t nonzero elements of G occurring lambda times, and the other v-1-t occurring lambda+1 times. When lambda=0 , this is equivalent to a modular Golomb ruler. In this paper we investigate existence questions on these objects, and extend previous results constructing almost difference sets by adding or removing an element from a difference set. We also show for which primes the octic residues, with or without zero, form an almost difference set.

A (v, k, lambda) difference set in a group G is a subset {d(1), d(2), . . . , dk} of G such that D = Sigma d(i) in the group ring Z[G] satisfies DD-1 = n + lambda G where n= k - lambda. If D = Sigma s(i)d(i), where the s(i) is an element of{+/- 1}, satisfies the same equation, we will call it a signed difference set. This generalizes both difference sets (all s(i) = 1) and circulant weighing matrices (G cyclic and lambda = 0). We will show that there are other cases of interest, and give some results on their existence.

Objectives: To evaluate the rates of myopericarditis (primary objective) and rates of cardiovascular and neurological adverse events (secondary objectives) in temporal association with ACAM2000 (R) smallpox vaccine. Methods: Observational cohort study conducted through monthly surveillance from 2009 to 2017 of electronic medical records of military service members (SM) for pre-specified cardiac and neurological International Classification of Diseases (ICD) codes reported in the 30 days following smallpox vaccination. ICD codes potentially predictive of myopericarditis and codes for encephalitis, Guillain-Barre syndrome, and sudden death were classified into Group 1. All other cardiovascular and neurological ICD codes were classified into Group 2. Medical records containing Group 1 codes were individually reviewed to confirm coding accuracy and to seek additional data in support of myopericarditis adjudication, which was performed by an independent clinical panel. Chart reviews were not performed for Group 2 codes, which were reported in aggregate only. Results: 897,227 SM who received ACAM2000 smallpox vaccine and 450,000 SM who received Dryvax smallpox vaccine were included in the surveillance population. The rate of adjudicated myopericarditis among ACAM2000 smallpox vaccine recipients was 20.06/100,000 and was significantly higher for males (21.8/100,000) than females (8.5/100,000) and for those < 40 years of age (21.1/100,000) than for those 40 years or older (6.3/100,000). Overall rates for any cardiovascular event (Group 1 plus Group 2) were 113.5/100,000 for ACAM2000 vaccine and 439.3/100,000 for Dryvax vaccine; rate ratio, 0.26 (95% CI, 0.24-0.28). The rates of subjects with one or more defined neurological events were 2.12/100,000 and 1.11/100,000 for ACAM2000 and Dryvax vaccines respectively; rate ratio, 1.91 (95% CI, 0.71-5.10). Conclusions: Electronic records surveillance of the entire vaccinated SM population over a ten-year period found rates of myopericarditis, of defined neurological events, and of overall cardiac events that were consistent with those of prior passive surveillance studies involving Dryvax or ACAM2000 smallpox vaccines. (C) 2021 Elsevier Ltd. All rights reserved.

A weighing matrix W = (wi,j) is a square matrix of order n and entries wi,j in {0,± 1} such that WWT = kIn. In his thesis, Strassler gave a table of existence results for circulant weighing matrices with n ≤ 200 and k ≤ 100. In the latest version of Strassler’s table given by Tan, there are 34 open cases remaining. In this paper we give nonexistence proofs for 12 of these cases, report on preliminary searches outside Strassler’s table, and characterize the known proper circulant weighing matrices.

Objectives: To compare rates of myopericarditis, severe and serious dermatological or neurological events, and other adverse events in deploying US military personnel who received or did not receive ACAM2000 (R) (Smallpox [Vaccinia] Vaccine, Live) vaccine and to evaluate potential risk factors for development of myopericarditis. Methods: Prospective observational cohort study enrolling up to 15,000 ACAM2000 recipients (Cohort 1) and up to 5000 persons otherwise eligible for ACAM2000 vaccination but not vaccinated due to recency of vaccination or characteristics of their contacts (Cohort 2). Data and specimens were collected initially and 10 (6-17) days later. Those with clinical or laboratory evidence of possible myopericarditis were referred for further evaluation and adjudication by a blinded independent review committee. The adjusted odds ratio for myopericarditis was determined by a logistic regression model controlling for age, race, gender, and exercise regimen. Results: 14,667 subjects provided initial data and specimens (Cohort 1, 10,825; Cohort 2, 3842); 12,110 (Cohort 1, 8945; Cohort 2, 3165) completed Visit 2 per-protocol. A total of 125 (Cohort 1, 111; Cohort 2, 14) were referred for myopericarditis adjudication, yielding 54 (Cohort 1, 44, Cohort 2, 10) subclinical myopericarditis, 5 suspected myocarditis, 1 confirmed myocarditis, and 1 suspected pericarditis. Unadjusted myopericarditis rates were: Cohort 1, 5.7/1000 (95% CI, 4.3-7.5); Cohort 2, 3.2/1000 (95% CI, 1.7-5.8). Unadjusted and adjusted odds ratios for myopericarditis were 1.8 (95% CI: 0.9-3.6) and 1.3 (95% CI: 0.6-2.6), respectively. One hundred seventeen subjects (1.1%) in Cohort 1 and 13 (0.3%) in Cohort 2 experienced at least 1 serious adverse event. No instances of serious and severe neurological or dermatological adverse events were reported. Conclusions: In this carefully screened, generally young and healthy service-member population, ACAM2000 vaccination was associated with modest non-significant increases in the risk of myopericarditis (adjusted OR, 1.3; unadjusted OR, 1.8); all but seven cases were subclinical. (C) 2020 Elsevier Ltd. All rights reserved.

In a 1989 paper \cite{arasu2}, Arasu used an observation about multipliers to show that no $(352,27,2)$ difference set exists in any abelian group. The proof is quite short and required no computer assistance. We show that it may be applied to a wide range of parameters $(v,k,\lambda)$, particularly for small values of $\lambda$. With it a computer search was able to show that the Prime Power Conjecture is true up to order $2 \cdot 10^{10}$, extend Hughes and Dickey's computations for $\lambda=2$ and $k \leq 5000$ up to $10^{10}$, and show nonexistence for many other parameters.

We review the current status of the multiplier conjecture for difference sets, present some new results on it, and determine the open cases of the conjecture for abelian groups of order \(<\)10\(^6\). It turns out that for Paley parameters \((4n-1,2n-1,n-1,n)\), where \(4n-1\) is a prime power, the validity of the multiplier conjecture can be verified in the vast majority of cases, while for other parameter sets numerous cases remain open.

Let $S(x)$ be the number of $n \leq x$ for which a Hadamard matrix of order $n$ exists. Hadamard's conjecture states that $S(x)$ is about $x/4$. From Paley's constructions of Hadamard matrices, we have that \[ S(x) = \Omega(x/\log x). \] In a recent paper, the first author suggested that counting the products of orders of Paley matrices would result in a greater density. In this paper we use results of Kevin Ford to show that it does: \begin{equation}\label{eq:abs} S(x) \geq x/\log x \exp((C+o(1))(\log \log \log x)^2)\,, \nonumber \end{equation} where $C=0.8178...$. This bound is surprisingly hard to improve upon. We show that taking into account all the other major known construction methods for Hadamard matrices does not shift the bound. Our arguments use the notion of a (multiplicative) monoid of natural numbers. We prove some initial results concerning these objects. Our techniques may be useful when assessing the status of other existence questions in design theory.

One way to find near-matches in large datasets is to use hash functions. In recent years locality-sensitive hash functions for various metrics have been given; for the Hamming metric projecting onto k bits is simple hash function that performs well. In this paper, we investigate alternatives to projection. For various parameters hash functions given by complete decoding algorithms for error-correcting codes work better, and asymptotically random codes perform better than projection.

Background: Immunization with RTS,S/AS02 consistently protects some vaccinees against malaria infection in experimental challenges and in field trials. A brief immunization schedule against falciparum malaria would be compatible with the Expanded Programme on Immunization, or in combination with other prevention measures, interrupt epidemic malaria or protect individuals upon sudden travel to an endemic area.Methods: We conducted an open label, Phase 2a trial of two different full dose schedules of RTS,S/AS02 in 40 healthy malaria-naive adults. Cohort 1 (n=20) was immunized on a 0, 1, and 3 month schedule and Cohort 2 (n = 20) on a 0, 7, and 28 day schedule. Three weeks later, 38 vaccinees and 12 unimmunized infectivity controls underwent malaria challenge.Results: Both regimens had a good safety and tolerability profile. Peak GMCs of antibody to the circumsporozoite protein (CSP) were similar in Cohort 1 (78 mu g/mL; 95% CI: 45-134) and Cohort 2 (65 mu g/mL; 95% CI: 40-104). Vaccine efficacy for Cohort 1 was 45% (95% CI: 18-62%) and for Cohort 2, 39% (95% CI: 11-56%). Protected volunteers had a higher GMC of anti-CSP antibody (114 mu g/mL) than did volunteers with a 2-day delay (70 mu g/mL) or no delay (30 mu g/mL) in the time to onset of parasitemia (Kruskal-Wallis, p = 0.019). A trend was seen for higher CSP-specific IFN-gamma responses in PBMC from protected volunteers only in Cohort 1, but not in Cohort 2, for ex vivo and for cultured ELISPOT assays.Conclusion: In malaria-naive adults, the efficacy of three-dose RTS,S/AS02 regimens on either a 0, 1, and 3 month schedule or an abbreviated 0, 7, and 28 day schedule was not discernibly different from two previously reported trials of two-dose regimens given at 0, 1 month that conferred 47% (95% CI: - 19 to 76%) protection and in another trial 42% (95% CI: 5-63%). A strong association of CSP-specific antibody with protection against malaria challenge is observed and confirms similar observations made in other studies. Subsequent trials of adjuvanted RTS,S in African children and infants on a 0, 1, and 2 month schedule have demonstrated a favorable safety and efficacy profile. Published by Elsevier Ltd.

Discrete event simulation is widely used in performance and dependability analysis of systems, often in a way that many replica of a model are simulated. Those replica may reveal substantially different dynamic behavior of the simulation model. Recognizing if this is the case and what different classes of behavior are present can be of relevance to gain more insight in the system under study but also to recognize errors that may be present in a simulation model. Trace analysis is a classic technique to figure out what happens in a single simulation run. In this paper, we discuss work in progress on clustering a set of simulation traces. The outcome helps a modeler to select traces that suggest themselves for an individual and detailed analysis either as being representative for a whole class of traces or being an outstanding extraordinary case.

Delsarte conjectured in 1973 that there are no nontrivial pefect codes in the Johnson scheme. Etzion and Schwartz recently showed that perfect codes must be k-regular for large k, and used this to show that there are no perfect codes correcting single errors in J(n,w) for n les 50 000. In this correspondence we show that there are no perfect single error-correcting codes for n les 2 250

Call a set of integers b 1, b 2,..., b k admissible if for any prime p, at least one congruence class modulo p does not contain any of the b i. Let ρ *(x) be the size of the largest admissible set in [1, x]. The Prime k-tuples Conjecture states that any for any admissible set, there are infinitely many n such that n+b 1,... n+b 2, n+b k are simultaneously prime. In 1974, Hensley and Richards [3] showed that ρ *(x)>π(x) for x sufficiently large, which shows that the Prime k-tuples Conjecture is inconsistent with a conjecture of Hardy and Littlewood that for all integers x,y ≥ 2, π (x + y) ⩽π (x) + π (y). In this paper we examine the behavior of ρ *(x), in particular, the point at which ρ *(x) first exceeds π(x), and its asymptotic growth.

Previous surveys by Baumert and Lopez and Sanchez have resolved the existence of cyclic (v,k,lambda) difference sets with k <= 150, except for six open cases. In this paper we show that four of those difference sets do not exist. We also look at the existence of difference sets with k <= 300 and cyclic Hadamard difference sets with v <= 10,000. Finally, we extend an earlier search of the second author to show that no cyclic projective planes exist with non-prime power orders up to two billion.

From the *Malaria Program, Naval Medical Research Institute, Bethesda, Maryland 20889; the :~Department of Molecular Microbiology and Immunology, School of Hygiene and Public Health, The Johns Hopkins University, Baltimore, Maryland 21205; w Torrey Pines Institute for Molecular Studies and Houghten Pharmaceuticals Inc., San Diego, California 92121; the [[Laboratory of Molecular Structure, National Institute of Allergy and Infectious Diseases, National Institutes of Health, Rockville, Maryland 20852; and the ~ Department of Immunology, Walter Reed Army Institute of Research, Washington, DC 20307

Fix n. Let r(n) denote the largest number r for which there is an r×n (1, ?1)-matrix H satisfying the matrix equation HH?=nIr. The Hadamard conjecture states that for n divisible by 4 we have r(n)=n. Let ?>0. In this paper, we show that the Extended Riemann Hypothesis and recent results on the asymptotic existence of Hadamard matrices imply that for n sufficiently large r(n)>(12??)n.

Using a number field sieve, discrete logarithms modulo primes of special forms can be found faster than standard primes. This has raised concerns about trapdoors in discrete log cryptosystems, such as the Digital Signature Standard. This paper discusses the practical impact of these trapdoors, and how to avoid them.

Let A(n,d) denote the greatest number of codewords possible in a binary block code of length n and distance d. Plotkin gave a simple counting argument which leads to an upper bound B(n,d) for A(n,d) when d>n/2. Levenshtein (1964) proved that if Hadamard's conjecture is true then Plotkin's bound is sharp. Though Hadamard's conjecture is probably true, its resolution remains a difficult open question. So it is natural to ask what one can prove about the ratio R(n,d)=A(n,d)/B(n,d). This note presents an efficient heuristic for constructing, for any d/spl ges/n/2, a binary code which has at least 0.495B(n,d) codewords. A computer calculation confirms that R(n,d)>0.495 for d up to one trillion.

We give an efficient algorithm for factoring polynomials over finite algebraic extensions of the ρ-adic numbers. This algorithm uses ideas of Chistov’s random polynomial-time algorithm, and is suitable for practical implementation.