Integer Weights Research Articles

On Doi–Naganuma and Shimura liftings

In this paper, we extend the Doi–Naganuma lifting to higher levels by following the methods of Zagier and Kohnen. We prove that there is a Hecke-equivariant linear map from the space of elliptic cusp forms of integer weight k, level $$N, ((N,D)=1)$$ to Hilbert cusp forms of weight k, level N associated to a real quadratic field of discriminant D ( $$D\equiv 1\pmod {4}$$ ) with class number one. The above lifting is obtained by computing the explicit image of Poincare series of weight k, level N for the cusp at $$\infty $$ . Finally, we see that the above lifting is closely related to the Dth Shimura lift on the Kohnen plus space.

Association of an Electroencephalography-Based Risk Score With Seizure Probability in Hospitalized Patients

Continuous electroencephalography (EEG) use in critically ill patients is expanding. There is no validated method to combine risk factors and guide clinicians in assessing seizure risk. To use seizure risk factors from EEG and clinical history to create a simple scoring system associated with the probability of seizures in patients with acute illness. We used a prospective multicenter (Emory University Hospital, Brigham and Women's Hospital, and Yale University Hospital) database containing clinical and electrographic variables on 5427 continuous EEG sessions from eligible patients if they had continuous EEG for clinical indications, excluding epilepsy monitoring unit admissions. We created a scoring system model to estimate seizure risk in acutely ill patients undergoing continuous EEG. The model was built using a new machine learning method (RiskSLIM) that is designed to produce accurate, risk-calibrated scoring systems with a limited number of variables and small integer weights. We validated the accuracy and risk calibration of our model using cross-validation and compared its performance with models built with state-of-the-art logistic regression methods. The database was developed by the Critical Care EEG Research Consortium and used data collected over 3 years. The EEG variables were interpreted using standardized terminology by certified reviewers. All patients had more than 6 hours of uninterrupted EEG recordings. The main outcome was the average risk calibration error. There were 5427 continuous EEGs performed on 4772 participants (2868 men, 49.9%; median age, 61 years) performed at 3 institutions, without further demographic stratification. Our final model, 2HELPS2B, had an area under the curve of 0.819 and average calibration error of 2.7% (95% CI, 2.0%-3.6%). It included 6 variables with the following point assignments: (1) brief (ictal) rhythmic discharges (B[I]RDs) (2 points); (2) presence of lateralized periodic discharges, lateralized rhythmic delta activity, or bilateral independent periodic discharges (1 point); (3) prior seizure (1 point); (4) sporadic epileptiform discharges (1 point); (5) frequency greater than 2.0 Hz for any periodic or rhythmic pattern (1 point); and (6) presence of "plus" features (superimposed, rhythmic, sharp, or fast activity) (1 point). The probable seizure risk of each score was 5% for a score of 0, 12% for a score of 1, 27% for a score of 2, 50% for a score of 3, 73% for a score of 4, 88% for a score of 5, and greater than 95% for a score of 6 or 7. The 2HELPS2B model is a quick accurate tool to aid clinical judgment of the risk of seizures in critically ill patients.

Representations of the Kauffman bracket skein algebra, II: Punctured surfaces

In earlier work, we constructed invariants of irreducible representations of the Kauffman skein algebra of a surface. We introduce here an inverse construction, which to a set of possible invariants associates an irreducible representation that realizes these invariants. The current article is restricted to surfaces with at least one puncture, a condition that will be lifted in subsequent work of the authors that relies on this one. A step in the proof is of independent interest, and describes the algebraic structure of the Thurston intersection form on the space of integer weight systems for a train track.

Weight-Balanced Timed Event Graphs to Model Periodic Phenomena in Manufacturing Systems

Timed event graphs (TEGs) are suitable to model manufacturing systems in which synchronization and delay phenomena appear. Since 1980s, TEGs are studied as a class of linear discrete event systems in idempotent semirings such as the (min,+) algebra. In this paper, we consider the class of weighted TEGs (WTEGs) that corresponds to TEGs where the edges have integer weights. By introducing nonunitary weights, WTEGs widen the class of manufacturing systems that can be modeled, especially systems with batches and duplications. Moreover, a subclass of WTEGs called weight-balanced TEGs (WB-TEGs) can be studied with the algebraic tools that stem from the theory of (min,+) linear systems. In this paper, the focus lies on some modeling issues for manufacturing systems. Besides cutting and palletization operations, it is shown that WB-TEGs are also well adapted to describe periodic routing policies and, in a symmetrical way, how to merge flows similar to a multiplexer. In order to simplify the modeling step, a class of cycloweighted TEGs (CW-TEGs) is introduced. It is an extension of WTEGs where the weights of the edges can change according to a periodic sequence. Finally, we propose some elements of modeling that can be described by CW-TEGs or equivalently with an input–output transfer relation in an appropriate idempotent semiring of operators. Note to Practitioners — The (min,+) linear system theory used in this paper aims at obtaining linear models for a subclass of man-designed systems, such as automated manufacturing systems or traffic networks. This theory has many analogies with the conventional linear system theory (for continuous systems) and it provides the basis to develop a specific control theory for man-made systems. More precisely, the theory of (min,+) linear systems is well suited to systems where the prevailing phenomena are synchronizations, delays, duplications, and batches. These phenomena arise, for example, in operations such as assembly/matching, cutting/lot splitting, and palletization/lot making. Among the possible representations, we can describe these systems by transfer functions obtained by the combination of a finite number of basic operators. This is analogous to block diagram in the conventional system theory, i.e., a transfer function describes the complete input-output behavior of a system. In the context of manufacturing systems, a transfer function describes the way a system maps an input flow of materials (raw part inputs) into an output flow (finished parts), without the necessity of simulation tools to predict this. Moreover, the transfer function thus obtained can be used to compute controllers in order to regulate the internal flows of a system, for instance to decrease internal stocks. In the case of an automated system, the obtained controllers can be implemented on a programmable logic controller as supplementary code. This paper focuses on the use of these algebraic tools in the model process of manufacturing systems and, in particular, on their ability to describe splitting and merging flows of materials.

Conjugacy growth series for wreath product finitary symmetric groups

In recent work, Bacher and de la Harpe define and study conjugacy growth series for finitary permutation groups. In two subsequent papers, Cotron, Dicks, and Fleming study the congruence properties of some of these series. We define a new family of conjugacy growth series for the finitary alternating wreath product that are related to sums of modular forms of integer and half-integral weights, the so-called mixed weight modular forms. The previous works motivate the study of congruences for these series. We prove that congruences exist modulo powers of all primes p ge 5. Furthermore, we lay out a method for studying congruence properties for sums of mixed weight modular forms in general.

Asymptotic vulnerability of positional voting rules to coalitional manipulation

Voting rule performances are sometimes evaluated according to their respective resistances to allow profitable misrepresentation of individual preferences. This seems to be a hard task when scoring systems with possibly non integer weights are involved. In this paper, it is shown how one can still obtain asymptotic results in these settings. Our analysis for three-candidate elections provides a characterization of unstable voting situations at which a positional voting rule is manipulable by some coalition not larger than an arbitrary proportion of the electorate. This allows us to address a conjecture by Pritchard and Wilson (2007). That is, under the Impartial Anonymous Culture (IAC), the plurality rule asymptotically minimizes the vulnerability to coalitional manipulation when the size of the manipulating coalition is unrestricted. This later result is no longer valid when only manipulation by small coalitions is considered: now, the Borda rule tends to outperform other rules. Furthermore, the vulnerability of a positional voting rule to coalitional manipulation is not affected by increasing the size of the manipulating coalition from 0.5 to 1.

Denoising Signals Used in Gas Turbine Diagnostics with Ant Colony Optimized Weighted Recursive Median Filters

Accurate fault detection and isolation requires signal processing of measurement signals which are contaminated with noise. Typically, gas turbine faults are revealed by sharp trend shifts in the signals and these trend shifts should be preserved during signal processing. Linear filters can smooth out the sharp trend shifts while removing noise. However, nonlinear filters such as the weighted recursive median (WRM) filters show good noise reduction while preserving key signal features if their integer weights are determined optimally. We propose the ant colony optimization (ACO) method coupled with local search to calculate the integer weights of WRM filters. It is found that the filter weight optimization problem is mathematically equivalent to the quadratic assignment problem which can be solved by ACO. Optimal parameters for the ACO are found using numerical experiments. The WRM filter is demonstrated for abrupt and gradual faults in gas turbines and is found to yield noise reduction of 52–64% for simulated noisy signals considered in this paper.

A new equivariant in nonarchimedean dynamics

Let K be a complete, algebraically closed, nonarchimedean valued field, and let f(z) be a rational function in K(z) of degree d at least 2. We show there is a natural way to assign non-negative integer weights w_f(P) to points of the Berkovich projective line over K, in such a way that the sum over all points is d-1. When f(z) has bad reduction, the set of points with nonzero weight forms a distributed analogue of the single point which occurs when f(z) has potential good reduction. Using this, we characterize the Minimal Resultant Locus of f(z) in dynamical and moduli-theoretic terms: dynamically, it is the barycenter of the weight-measure attached to f(z); moduli-theoretically, it is the closure of the set of type II points where f(z) has semi-stable reduction in the sense of Geometric Invariant Theory.

The Computational Power of Neural Networks and Representations of Numbers in Non-Integer Bases

We briefly survey the basic concepts and results concerning the computational power of neural net-orks which basically depends on the information content of eight parameters. In particular, recurrent neural networks with integer, rational, and arbitrary real weights are classi ed within the Chomsky and finer complexity hierarchies. Then we re ne the analysis between integer and rational weights by investigating an intermediate model of integer-weight neural networks with an extra analog rational-weight neuron (1ANN). We show a representation theorem which characterizes the classification problems solvable by 1ANNs, by using so-called cut languages. Our analysis reveals an interesting link to an active research field on non-standard positional numeral systems with non-integer bases. Within this framework, we introduce a new concept of quasi-periodic numbers which is used to classify the computational power of 1ANNs within the Chomsky hierarchy.

Package-X 2.0: A Mathematica package for the analytic calculation of one-loop integrals

This article summarizes new features and enhancements of the first major update of Package-X. Package-X 2.0 can now generate analytic expressions for arbitrarily high rank dimensionally regulated tensor integrals with up to four distinct propagators, each with arbitrary integer weight, near an arbitrary even number of spacetime dimensions, giving UV divergent, IR divergent, and finite parts at (almost) any real-valued kinematic point. Additionally, it can generate multivariable Taylor series expansions of these integrals around any non-singular kinematic point to arbitrary order. All special functions and abbreviations output by Package-X 2.0 support Mathematica’s arbitrary precision evaluation capabilities to deal with issues of numerical stability. Finally, tensor algebraic routines of Package-X have been polished and extended to support open fermion chains both on and off shell. The documentation (equivalent to over 100 printed pages) is accessed through Mathematica’s Wolfram Documentation Center and contains information on all Package-X symbols, with over 300 basic usage examples, 3 project-scale tutorials, and instructions on linking to FeynCalc and LoopTools. New version program summaryProgram title: Package-XProgram files doi:http://dx.doi.org/10.17632/yfkwrd4d5t.1Licensing provisions: CC by 4.0Programming language: Mathematica (Wolfram Language)Journal reference of previous version: H. H. Patel, Comput. Phys. Commun 197, 276 (2015)Does the new version supersede the previous version?: YesSummary of revisions: Extension to four point one-loop integrals with higher powers of denominator factors, separate extraction of UV and IR divergent parts, testing for power IR divergences, construction of Taylor series expansions of one-loop integrals, numerical evaluation with arbitrary precision arithmetic, manipulation of fermion chains, improved tensor algebraic routines, and much expanded documentation.Nature of problem: Analytic calculation of one-loop integrals in relativistic quantum field theory.Solution method: Passarino–Veltman reduction formula, Denner–Dittmaier reduction formulae, and additional algorithms described in the manuscript.Restrictions: One-loop integrals are limited to those involving no more than four denominator factors.

The World Health Organization Adult Attention-Deficit/Hyperactivity Disorder Self-Report Screening Scale for DSM-5

Recognition that adult attention-deficit/hyperactivity disorder (ADHD) is common, seriously impairing, and usually undiagnosed has led to the development of adult ADHD screening scales for use in community, workplace, and primary care settings. However, these scales are all calibrated to DSM-IV criteria, which are narrower than the recently developed DSM-5 criteria. To update for DSM-5 criteria and improve the operating characteristics of the widely used World Health Organization Adult ADHD Self-Report Scale (ASRS) for screening. Probability subsamples of participants in 2 general population surveys (2001-2003 household survey [n = 119] and 2004-2005 managed care subscriber survey [n = 218]) who completed the full 29-question self-report ASRS, with both subsamples over-sampling ASRS-screened positives, were blindly administered a semistructured research diagnostic interview for DSM-5 adult ADHD. In 2016, the Risk-Calibrated Supersparse Linear Integer Model, a novel machine-learning algorithm designed to create screening scales with optimal integer weights and limited numbers of screening questions, was applied to the pooled data to create a DSM-5 version of the ASRS screening scale. The accuracy of the new scale was then confirmed in an independent 2011-2012 clinical sample of patients seeking evaluation at the New York University Langone Medical Center Adult ADHD Program (NYU Langone) and 2015-2016 primary care controls (n = 300). Data analysis was conducted from April 4, 2016, to September 22, 2016. The sensitivity, specificity, area under the curve (AUC), and positive predictive value (PPV) of the revised ASRS. Of the total 637 participants, 44 (37.0%) household survey respondents, 51 (23.4%) managed care respondents, and 173 (57.7%) NYU Langone respondents met DSM-5 criteria for adult ADHD in the semistructured diagnostic interview. Of the respondents who met DSM-5 criteria for adult ADHD, 123 were male (45.9%); mean (SD) age was 33.1 (11.4) years. A 6-question screening scale was found to be optimal in distinguishing cases from noncases in the first 2 samples. Operating characteristics were excellent at the diagnostic threshold in the weighted (to the 8.2% DSM-5/Adult ADHD Clinical Diagnostic Scale population prevalence) data (sensitivity, 91.4%; specificity, 96.0%; AUC, 0.94; PPV, 67.3%). Operating characteristics were similar despite a much higher prevalence (57.7%) when the scale was applied to the NYU Langone clinical sample (sensitivity, 91.9%; specificity, 74.0%; AUC, 0.83; PPV, 82.8%). The new ADHD screening scale is short, easily scored, detects the vast majority of general population cases at a threshold that also has high specificity and PPV, and could be used as a screening tool in specialty treatment settings.

A linear weighted (n, f, k) system for non-homogeneous Markov-dependent components

ABSTRACTWe study a linear weighted (n, f, k) system, denoted by L(n, f, k, w) system and consider the situation where components are non-homogeneous Markov-dependent. An L(n, f, k, w) system consists of n components ordered in a line, and each component u has a positive integer weight wu for u = 1, 2, …, n and w = (w1, w2, …, wn). The L(n, f, k, w):F (G) system fails (works) if the total weight of failed (working) components is at least f or the total weight of consecutive failed (working) components is at least k. For the L(n, f, k, w):F system with non-homogeneous Markov-dependent components, we derive closed-form formulas for the system reliability, the marginal reliability importance measure of a single component, and the joint reliability importance measure of multiple components using a conditional probability generating function method. We extend these results to the L(n, f, k, w):G systems, the weighted consecutive-k-out-of-n systems, and the weighted f-out-of-n systems. Our numerical examples and a case study on a bridge system demonstrate the use of derived formulas and provide the insights on the L(n, f, k, w) systems and the importance measures. In addition, the two failure modes associated with the L(n, f, k, w):F systems are analyzed by comparing to the single failure mode associated with the weighted consecutive-k-out-of-n:F systems and the single failure mode associated with the weighted f-out-of-n:F systems.

The adjoint map of the Serre derivative and special values of shifted Dirichlet series

We compute the adjoint of the Serre derivative map with respect to the Petersson scalar product by using existing tools of nearly holomorphic modular forms. The Fourier coefficients of a cusp form of integer weight k, constructed using this method, involve special values of certain shifted Dirichlet series associated with a given cusp form f of weight k+2. As application, we get an asymptotic bound for the special values of these shifted Dirichlet series and also relate these special values with the Fourier coefficients of f. We also give a formula for the Ramanujan tau function in terms of the special values of the shifted Dirichlet series associated to the Ramanujan delta function.

Difference dimension quasi-polynomials

We consider Hilbert-type functions associated with difference (not necessarily inversive) field extensions and systems of algebraic difference equations in the case when the translations are assigned some integer weights. We will show that such functions are quasi-polynomials, which can be represented as alternating sums of Ehrhart quasi-polynomials associated with rational conic polytopes. In particular, we obtain generalizations of main theorems on difference dimension polynomials and their invariants to the case of weighted basic difference operators.

Stable Sets in {ISK4,wheel}-Free Graphs

An ISK4 in a graph G is an induced subgraph of G that is isomorphic to a subdivision of K_4 (the complete graph on four vertices). A wheel is a graph that consists of a chordless cycle, together with a vertex that has at least three neighbors in the cycle. A graph is {ISK4,wheel}-free if it has no ISK4 and does not contain a wheel as an induced subgraph. We give an O(|V(G)|^7)-time algorithm to compute the maximum weight of a stable set in an input weighted {ISK4,wheel}-free graph G with non-negative integer weights.

An Integer Weighted Genomic Mutation Scoring (IWGMS) Using the Trusight Myeloid Sequencing Panel (Illumina) Shows Higher Mortality in Patients with Intermediate Risk Acute Myeloid Leukemia- a Retrospective Study

Background: Acute Myeloid Leukemia (AML) without favorable and particular unfavorable cytogenetic aberrations is classified as intermediate prognosis. Recurrent somatic genomic mutations through The Cancer Genome Atlas (TCGA) have provided valuable prognostic information in AML. There are very few studies that have incorporated the cytogenetics (Cy), Next Generation sequencing (NGS) and Overall Survival (OS) in AML. Moreover prognostic NGS studies have a limited collective context without a quantifiable stratification. For the purpose of prognostic risk stratification, we utilized the TCGA data by Ley et.al and developed a system of Integer Weights for the Genomic Mutation Score (IWGMS) obtained by targeted NGS at Houston Methodist Hospital. We then correlated the IWGMS with patients' outcomes in a retrospective manner.Methods: The patient data was queried from METEOR (Methodist Environment for Translational Enhancement and Outcomes Research), a clinical data warehouse that integrates existing data with internal and external research databases and national registries. We queried for the diagnosis of AML and demographics, Cy, NGS and OS. We divided the patients into 3 groups according to their MRC cytogenetic risks- Favorable (FCy), Intermediate (ICy), Poor (PCy)). Mutations in 54 genes associated with myeloid disorders were tested in NGS by using the TruSight Myeloid Sequencing Panel (Illumina) (Table 1). Briefly, genomic DNA was extracted from sorted specimens using automated methods on the MagnaPure Compact instrument (Roche Diagnostics). Sequencing libraries were prepared using TruSight reagents and sequenced on a MiSeq instrument using a 2x300 bp paired end strategy. Read alignment and variant calling for minimum of 100x amplicon coverage was performed using VariantStudio Software (Illumina). The biologic significance of detected variants was determined using VarView5 (an in-house developed bioinformatics tool). Interpretations are reviewed in a consensus conference. For the data described herein, interpretations were limited to known nonsynonymous (single nucleotide polymorphsims and insertions or deletions) somatic mutations.Results: Of the 1200 AML patients reviewed, 100 patients meet the criteria for having the information on Cy and NGS. The mortality rate for FCy, ICy and PCy groups are 43%, 52%, and 51% respectively. IWGMS was designed by assigning a score for each genomic mutation between the range of negative 2 (-2) for good risk to positive 2 (+2) for each of 9 TCGA mutation categories (Transcription- Factor Fusion, Nucleophosmin (NPM1), Tumor Suppressor Genes, DNA-Methylation related genes, Signaling Genes, Chromatin Modifying Genes, Myeloid Transcription Factor Genes, Cohesion complex Genes and Spliceosome-complex genes). The total IWGMS for each patient was calculated by the sum of mutation scores in each 9 categories. The score greater than 3 was defined as high risk. By univariate analysis, in the ICy, high IWGMS was associated with significantly higher mortality rate than low IWGMS (80% vs 44%, p=0.045). In PCy, patients with high IWGMS and low IWGMS had similar mortality rate (50% vs 52%, p=0.910) (Table 1).Conclusions: We have developed an IWGMS system to stratify patients with ICy into high and low risk groups. Our result demonstrated the significance of high mutation score in this group of patients, which will impact the management. The identification of genomic alterations along with the scoring system has a great potential for developing rationally-targeted therapies and improving outcomes. Further analysis along with the treatment outcomes will be presented at the ASH meeting in San Diego. [Display omitted] DisclosuresRice:Novartis Pharma: Speakers Bureau; Alexion: Membership on an entity's Board of Directors or advisory committees, Other: Participation in registry studies; Apellis/Synergy: Other: Data Safety Monitoring Committee member; Ablynx: Other: Participation in multi-center research trial; Selexys: Other: Participation in multi-center research trial; Incyte: Other: Participation in multi-center research trial. Iyer:Genentech: Research Funding; Seattle Genetics: Research Funding; BMS: Research Funding; Incyte: Research Funding; Arog: Research Funding; Celgene: Research Funding.

Vortices in a stochastic parabolic Ginzburg-Landau equation

We consider the variant of a stochastic parabolic Ginzburg-Landau equation that allows for the formation of point defects of the solution. The noise in the equation is multiplicative of the gradient type. We show that the family of the Jacobians associated to the solution is tight on a suitable space of measures. Our main result is the characterization of the limit points of this family. They are concentrated on finite sums of delta measures with integer weights. The singular set of the solution coincides with the points at which the delta measures are centered.

Moduli of curves, Gröbner bases, and the Krichever map

We study moduli spaces of (possibly non-nodal) curves (C,p1,…,pn) of arithmetic genus g with n smooth marked points, equipped with nonzero tangent vectors, such that OC(p1+…+pn) is ample and H1(OC(a1p1+…+anpn))=0 for given integer weights a=(a1,…,an) such that ai≥0 and ∑ai=g. We show that each such moduli space U˜g,nns(a) is an affine scheme of finite type, and the Krichever map identifies it with the quotient of an explicit locally closed subscheme of the Sato Grassmannian by the free action of the group of changes of formal parameters. We study the GIT quotients of U˜g,nns(a) by the natural torus action and show that some of the corresponding stack quotients give modular compactifications of Mg,n with projective coarse moduli spaces. More generally, using similar techniques, we construct moduli spaces of curves with chains of divisors supported at marked points, with prescribed number of sections, which in the case n=1 corresponds to specifying the Weierstrass gap sequence at the marked point.

Kontsevich–Zagier integrals for automorphic Green’s functions. II

In the framework of Kontsevich–Zagier periods, we derive integral representations for weight-k automorphic Green’s functions invariant under modular transformations in $$\varGamma _0(N)$$ ( $$N\,{\in }\,\mathbb Z_{\ge 1} $$ ), provided that there are no cusp forms on the respective Hecke congruence groups with an even integer weight $$k\ge 4$$ . These Kontsevich–Zagier integral representations for automorphic Green’s functions give explicit formulae for certain Eichler–Shimura maps connecting Eichler cohomology to Maas cusp forms. We construct integral representations for weight-4 Gross–Zagier renormalized Green’s functions (automorphic self-energy) from limit scenarios of the respective Kontsevich–Zagier integrals. We reduce the weight-4 automorphic self-energy on $$ X_0(4)(\mathbb C)=\varGamma _0(4)\backslash \mathfrak H^*$$ to an explicit form, which supports an algebraicity conjecture of Gross and Zagier.

Learning boolean halfspaces with small weights from membership queries

We consider the problem of proper learning of a boolean halfspace with integer weights {0,1,…,t}, from membership queries only. The best known algorithm for this problem is an adaptive algorithm that asks nO(t5) membership queries, while the best lower bound for the number of membership queries is nΩ(t)[1].In this paper we close this gap and give an adaptive proper learning algorithm with two rounds, and asking nO(t) membership queries. We also give a non-adaptive proper learning algorithm that asks nO(t3) membership queries.